Answer:
Step-by-step explanation:
10+5=15 1/9 goes into 15 about twice so it goes to plus 1
so about without solving is 16 1/15
Glen needs at least $225 for a new audio system. She he already saved $90. He earns $15 per hour at his part-time job. Write and solve an inequality to find how many hours he will need to work to buy the system.
Answer:
90+15x=225
Step-by-step explanation:
90 already saved plus 15 an hour equals 225
The radius of the wheel is 11 inches. What is the diameter of the wheel?
Answer:
22 inches
Step-by-step explanation:
Diameter = 2*radius = 2(11) = 22 inches
Find the average rate of change of the function between the given values of x.
y = -5x - x^2 between x = -5 and x = 7
Answer:
Use integrals to find the area between the curves.
32
3
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(
0
,
0
)
,
(
4
,
4
)
Equation Form:
x
=
0
,
y
=
0
x
=
4
,
y
=
4
To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius
f
(
x
)
and
A
=
π
r
2
.
V
=
π
∫
4
0
(
f
(
x
)
)
2
−
(
g
(
x
)
)
2
d
x
where
f
(
x
)
=
−
x
2
+
5
x
and
g
(
x
)
=
x
Simplify the integrand.
Tap for more steps...
V
=
x
4
−
10
x
3
+
24
x
2
Split the single integral into multiple integrals.
V
=
π
(
∫
4
0
x
4
d
x
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
4
with respect to
x
is
1
5
x
5
.
V
=
π
(
1
5
x
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Combine
1
5
and
x
5
.
V
=
π
(
x
5
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Since
−
10
is constant with respect to
x
, move
−
10
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
∫
4
0
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
3
with respect to
x
is
1
4
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
1
4
x
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Combine
1
4
and
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Since
24
is constant with respect to
x
, move
24
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
∫
4
0
x
2
d
x
)
By the Power Rule, the integral of
x
2
with respect to
x
is
1
3
x
3
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
(
1
3
x
3
]
4
0
)
)
Simplify the answer.
Tap for more steps...
V
=
384
π
5
The result can be shown in multiple forms.
Exact Form:
V
=
384
π
5
Decimal Form:
V
=
241.27431579
…
image of graph
To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius
f
(
x
)
and
A
=
π
r
2
.
V
=
π
∫
4
0
(
f
(
x
)
)
2
−
(
g
(
x
)
)
2
d
x
where
f
(
x
)
=
−
x
2
+
5
x
and
g
(
x
)
=
x
Simplify the integrand.
Tap for more steps...
V
=
x
4
−
10
x
3
+
24
x
2
Split the single integral into multiple integrals.
V
=
π
(
∫
4
0
x
4
d
x
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
4
with respect to
x
is
1
5
x
5
.
V
=
π
(
1
5
x
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Combine
1
5
and
x
5
.
V
=
π
(
x
5
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Since
−
10
is constant with respect to
x
, move
−
10
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
∫
4
0
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
3
with respect to
x
is
1
4
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
1
4
x
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Combine
1
4
and
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Since
24
is constant with respect to
x
, move
24
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
∫
4
0
x
2
d
x
)
By the Power Rule, the integral of
x
2
with respect to
x
is
1
3
x
3
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
(
1
3
x
3
]
4
0
)
)
Simplify the answer.
Tap for more steps...
V
=
384
π
5
The result can be shown in multiple forms.
Exact Form:
V
=
384
π
5
Decimal Form:
V
=
241.27431579
…
y
=
3
x
+
4
,
[
2
,
3
]
y
=
3
x
−
2
,
(
0
,
4
)
y
=
√
x
,
[
1
,
4
]
Step-by-step explanation:
Fresh Fruits sells 10 lemons for $2.50. What is the price for 1 lemon
Answer:
25 cents per lemon
Step-by-step explanation:
Simply divide
Answer:
See below
Step-by-step explanation:
When solving real world problems relating to unit price, divide the cost by the amount.
2.5/10
The unit price is 0.25.
-hope it helps
Which of the following choices are equivalent to the expression below? Check
all that apply.
318
A. (40)
B. x
c C. ()"
D. x
E. (88)
OF. (10)
Answer:
A
Step-by-step explanation:
because A is a Equivalent when you times it by 4
15. When working with the expression 6(2+.03) if we multiply first before adding, that is an example
of using the
property?
Answer:
Distributive Property
Step-by-step explanation:
If you multiply first,
6(2 + .03)
6•2 + 6•.03
You must multiply the 6 times BOTH of the terms inside the parenthesis.
This is using the Distributive Property.
Please help its due on friday
Answer:
28 cups
Step-by-step explanation:
If 7 cups will only fill 1/4 of her pot, multiply 4 by 7 to get 28.
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
I dont understand this question, i did the factor of 36x^2 - 49 but I dont understand the second part
Answer:
a = 6
b = 7
Step-by-step explanation:
Since both 36 and 49 are perfect squares, you can find their square roots which are 6 and 7.
To check to see if it is correct, replace the a with 6 and replace the b with 7, then evaluate the exponents.
what is 5a + 2/3= -1/6 with two step equations fractions
Answer:
-1/6
Step-by-step explanation:
5a+2/3=-1/6
5a=-1/6-2/3
5a=-1/6-4/6
5a=-5/6
a=(-5/6)/5
a=(-5/6)(1/5)
a=-5/30
simplify
a=-1/6
PLS HELP!! (40PTS.) (PRE-CALCULUS)
Step-by-step explanation:
All of these vectors are in DE Moviere Form, so let put them in Vector notation
To this this, multiply the modulus by the exact values of trig functions,
So using this, Vector u
[tex]u= 3j + 3 \sqrt{3} i[/tex]
Vector V
[tex]v = 2 \sqrt{2} j - 2 \sqrt{2} i[/tex]
Vector W
[tex]w = - 6 \sqrt{3}j + 6i[/tex]
So know we can compete the parts.
For Part A:
We first multiply the vector U by -7 then multiply that by v.
[tex] - 7u = - 21j - 21 \sqrt{3} j[/tex]
Know we do cross product
[tex] - 7u(v) = ( - 21j - 21 \sqrt{3} i)(2 \sqrt{2} j \: + 2 \sqrt{2} i[/tex]
First, multiply the j componets.
Then, do the I componets and then add the product together.
[tex] - 42 \sqrt{2} j - 42 \sqrt{6} i[/tex]
So the answer to part A is the vector above.
Part B:
Let first find the dot product of u and w.
First, the cross product of u and w is
[tex] - 18 \sqrt{3} j + 18\sqrt{3} i[/tex]
The magnitudes of each respective vector is
6 and -12. So if we use dot product formula
[tex] \cos( \alpha ) = \frac{xy}{ |x| |y| } [/tex]
So we get
[tex] \cos( \alpha ) = \frac{ - 18 \sqrt{3} + 18 \sqrt{3} }{ - 72} [/tex]
[tex] \cos(a) = \frac{0}{ - 12} [/tex]
[tex] \cos(a) = 0[/tex]
[tex]a = \frac{\pi}{2} [/tex]
Since the angle is pi/2, the vectors are orthogonal.
Answer:
correct
Step-by-step explanation:
Hello po ^^
⊱─━━━━━━━━⊱༻●༺⊰━━━━━━━━─⊰
Remember:
Correct answer = Brainliest
Complete answer = Brainliest
Perfect answer = Brainliest
[tex]\:\:\:\:\:[/tex]
Nonsense answer = Report
Wrong answer = Report
Incomplete answer = Report
⊱─━━━━━━━━⊱༻●༺⊰━━━━━━━━─⊰
Thank you!!
Quadrilaterals LMNO and STUV are similar. What is the value of x in inches?
A. 27.1
B. 9.2
C. 22.9
D. 6.6
Answer:
D
Step-by-step explanation:
2.2 : x = 4.1 : 12.3
2.2/x = 4.1/12.3 = 1/3
so x = 2.2 * 3 = 6.6
D
Find the missing value.
Hint: Use the number line to find the missing value.
-3=7-?
Answer:
X = 10
Step-by-step explanation:
-3=7-x
-7 -7
-10=-x
10=x
Need help with Geometry math
problem #9
Answer:
Let ABC be a triangle such that CA is produced to meet at E.
We know, an exterior angle of a Triangle is equal to non- adjacent interior angle, so
8x - 10 = x + 15 + 2x + 20
or, 8x - 3x = 35 + 10
or, 5x = 45
or, x = 9
copy machine makes 253 copies in 5 minutrs 45 seconds . How many per minute?
Answer:
46 copies I guess
Step-by-step explanation:
253÷5.45 =46
Correct me if i wrong
Answer:
46.422
Step-by-step explanation:
The answer is 46.422 because it's asking for how many copies per minute. And since we know there are 253 copies, we will divide 253 by 5.45. When you divide those you get 46.422
6. A person mailing postcards earns a fixed amount for each postcard he mails,
and yesterday his average hourly wage was $14.00 an hour. If he worked 5 hours
yesterday and mailed 300 postcards, how much does he earn for each postcard
mailed?
Answer:
If he worked 5 hours and his rate is $14/hr, then he earned a total of $70.He mailed 300 postcard, so each postcard mailed is $0.2333
Step-by-step explanation:
mark me brainliest!!
Find the equation of the line having a slope of 4 and a y-intercept on (0,3)
[tex]\mathbb{FINAL\:ANSWER:}[/tex]
[tex]\huge\boxed{\sf{y=4x+3}}[/tex]
[tex]\mathbb{SOLUTION\:WITH\:STEPS:}[/tex]
Hi! Hope you are having a nice day!
We are given the slope of the line and its y-intercept.
So, let's find the equation.
The y-intercept is written in the form (0, b).
No worries! b is the y-intercept.
Thus, the y-intercept equals 3.
Now, let's find the equation of the line with a slope of 4 and a y-intercept of 3.
We can write the equation in Slope-intercept form:
y=mx+b, where m stands for the slope and b stands for the y-intercept.
Since we have both m and b, we can just plug the given values:
y=4x+3 ✓
Hope you could understand everything.
#CarryOnLearning
Find the 40th term 360,353,346,...
Answer:
87
Step-by-step explanation:
First method:
- Open Excel and enter 360, 353 and 346 in column A (below each other)
- Select all 3 cells and drag the bottom-right square down to row 40.
Second method:
- Use the equation t(n) = 360-7(n-1)
- Solve for n=40
- t(40) = 360 - 7*39 = 87
3. Explain why (x – 4)2 = -9 has no real solutions.
Answer:
an equation is said to have no real solutions when value of x < 0
Step-by-step explanation:
here,
(x-4) 2= -9
2x - 8 = -9
2x = -1
x = -1/2
which is less than 0
The equation (x – 4)² = -9 has no real roots.
What is the solution of a quadratic equation?The solution of a quadratic equation is the value of the variable for which the expression becomes true.
Given,
(x – 4)² = -9
The LHS of the equation is either positive or zero.
But, the RHS of the equation is a negative value.
Therefore, RHS and LHS can never be equal.
Hence, the equation (x – 4)² = -9 has no real roots.
To learn more about quadratic equations visit:
https://brainly.com/question/17177510
#SPJ1
Please help
Use the distributive property to fill in the blanks below. 9x(7-2)=(_x7)-(_x2)
Answer:
9x(7-2)=(9x7)-(9x2)
Step-by-step explanation:
You're just multiplying 9 by the numbers inside the parenthesis... I hope this helps you :)
How to do this question
Answer:
b = 5
Step-by-step explanation:
Area of the triangle = b * 12/2 = 6b
Area of the rectangle = 9 * 12 = 108
Total area = 6b + 108 = 138
6b = 138 - 108 = 30
so b = 30/6 = 5
The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part. Give your answer as a completely simplified exact value in terms of π (no approximations).
57cm
because you get to subtract
AB of the right triangle ABC is twice the length of the leg BC. Find the number of degrees in angle ABC
Answer:
It is 45 degree angle
Step-by-step explanation:
AB is the tilted angle of the triangle
BC is the height and the vertical part of the triangle
If AB is 10 then BC is 5 and AC is possibly about 6-8
If that is so then 2 right triangles is a square
A square has 90 degree angles on any angle
Divide 90 by 2 which is 45 because a right triangle is half of a square
Therefore angle ABC is 45 degrees
Lesson 4.10 - Analytic Geometry
1) Prove that the following is a square. You must show all of your
work and give a written explanation of why the figure is a square. (First picture)
2) Prove that the following is a right - isosceles triangle. You must
show all of your work and give a written explanation of why the
figure is a right-isosceles triangle.
(Isosceles Triangles are triangles with 2 equal sides.) second picture
Geometric shapes are mathematical shapes that include squares and triangles
How to prove the shape is a squareThe side lengths of a square are congruent, and the adjacent sides are perpendicular.
So, we start by calculating the side lengths using the following distance formula
[tex]d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}[/tex]
Using the above formula, we have:
[tex]AB = \sqrt{(3-2)^2 + (4+2)^2} = \sqrt{37[/tex]
[tex]BC = \sqrt{(2+4)^2 + (-2+1)^2} = \sqrt{37[/tex]
[tex]CD = \sqrt{(-4+3)^2 + (-1-5)^2} = \sqrt{37}[/tex]
[tex]DA = \sqrt{(-3-3)^2 + (5-4)^2} = \sqrt{37}[/tex]
The above shows that the side lengths of the square are congruent.
Next, calculate the slope of the sides using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{AB} = \frac{4 +2}{3 -2} = 6[/tex]
[tex]m_{BC} = \frac{-2 + 1}{2+4} = -\frac 16[/tex]
[tex]m_{CD} = \frac{-1 -5}{-4+3} = 6[/tex]
[tex]m_{DA} = \frac{5 -4}{-3-3} = -\frac 16[/tex]
Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.
The above highlight, and the equal side lengths show that the figure (1) is a square
How to prove the shape is a right isosceles triangleThe legs of a right isosceles triangle are congruent, and the legs are perpendicular.
So, we start by calculating the lengths of the legs using the following distance formula
[tex]d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}[/tex]
Using the above formula, we have:
[tex]XY = \sqrt{(5-4)^2 + (-1-4)^2} = \sqrt{26[/tex]
[tex]XZ = \sqrt{(5-0)^2 + (-1+2)^2} = \sqrt{26[/tex]
The above shows that the legs of the right isosceles triangle are congruent.
Next, calculate the slope of the legs using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{XY} = \frac{5-4}{-1 -4} = -\frac{1}{5}[/tex]
[tex]m_{XZ} = \frac{5-0}{-1+2} = 5[/tex]
Notice that the slopes are opposite reciprocal.
The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle
Read more about geometric shapes at:
https://brainly.com/question/14285697
two friends share 1/2 of a pizza equally. What fraction of the pizza does each friend get?
Answer:
1/4
Step-by-step explanation:
In this equation, from the beginning we know two things, that there are two people, and that the whole is 1/2
So we just have to divide! Use this equation whenever dealing with word problems like these and you’re stuck.
Amount of object (Pizza Size) divided by Number of Groups (People) = Amount of object in group
So our equation is 1/2 divided by 2
Calculate this and we will get our final answer of
1/4!
Hope this helped and please award brainliest!
Consider the work sample and statements below. Select ALL that apply.
Answer:
A, B, D, F
Step-by-step explanation:
The work of solving the standard-form equation that is the difference of squares is properly shown except for Line 4. Statement [F] correctly describes the proper solution, which results in the solution set shown in Statement [B].
The first step was necessary to put the equation into standard form (Statement [D]). That form is the difference of squares (Statement [A]).
The statements that correctly describe the work are A, B, D, F.
How can 10% of 45 be used to determine 30% of 45?
Enter your answers in the boxes to correctly complete the sta
10% of 45 is
so 30% of 45 is
Answer: 10% of 45 is 4.5
So 30% of 45 is 13.5
Step-by-step explanation:
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 7 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches. Which of the following could be used to calculate the volume of water in the vase?
π(12in)2(3in) − 7(four over threeπ(1.5in)3)
π(3in)2(12in) − 7(four over threeπ(1.5in)3)
π(12in)2(3in) − 1.5(four over threeπ(7in)3)
π(3in)2(12in) − 1.5(four over threeπ(7in)3)
Answer:
Step-by-step explanation:
Vase:
h = 12 in
r = diameter/2 = 6/2 = 3 in
Volume of vase = πr²h
= π(3)²*12
Marbles:
r = 3/2 = 1.5 in
[tex]Volume \ of \ marbles = \dfrac{4}{3}\pi r^{3}\\\\\\Volume \ of \ 7 marbles=7*\dfrac{4}{3}\pi (1.5)^{3}[/tex]
Volume of water = Volume of vase - volume of 7 marbles
[tex]= \pi (3)^{2}*12 - 7*\dfrac{4}{3}\pi (1.5)^{3}[/tex]
Answer:
second choice
Step-by-step explanation:
the volume of water in the vase
= volume of the vase up to the height 12 inches - volume of 7 marbles
= π(6/2)²(12) - 7(4/3)π(3/2)³
so answer is the second choice
A pair of jeans cost £40 there is a discount of 15% on everything In the shop how much do the jeans cost after the discount
Answer:
34 Euros
Step-by-step explanation:
15% of 40 is 6.
40 minus 6 = 34
[tex][Hello,BrainlyUser][/tex]
Answer:
£34
Step-by-step explanation:
Given:
A pair of jeans cost £40
Discount of 15%
Question:
How much do the jeans cost after the discount
Solve:
£40 x 15% =6
£40 - 6 = 34
Hence, Jeans cost £34 after the discount
[CloudBreeze]
Evaluate the integral. (Use C for the constant of integration.)
2x^2+ 5x + 2/(x² + 1)2 dx
Answer:
[tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Method: U-Substitution
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite [Factor]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1) + 5x}{(x^2 + 1)^2}} \, dx[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1)}{(x^2 + 1)^2}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx[/tex][Left Integral] Simplify: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2}{x^2 + 1}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \int {\frac{1}{x^2 + 1}} \, dx + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx[/tex][Left Integral] Trigonometric Integration: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-substitution for the remaining integral.
Set u: [tex]\displaystyle u = x^2 + 1[/tex][u] Differentiate [Derivative Properties and Rules]: [tex]\displaystyle du = 2x \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{2x}{(x^2 + 1)^2}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{1}{u^2}} \, du[/tex]Apply Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{u} \bigg) + C[/tex][u] Back-substitute: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{x^2 + 1} \bigg) + C[/tex]Simplify: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C[/tex]∴ the integration of the given integral [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx[/tex] is equal to [tex]\displaystyle \bold{2 \arctan x - \frac{5}{2(x^2 + 1)} + C}[/tex].
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration