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# Find the integral $\int\frac{8x^2}{\left(x^{\left(3+2\right)}\right)^3}dx$

## Step-by-step Solution

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###  Videos

$-\frac{2}{3}x^{-12}+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{8x^2}{\left(x^{\left(3+2\right)}\right)^3}dx$

Specify the solving method

1

Simplify the expression inside the integral

$\int\frac{8}{x^{13}}dx$

Learn how to solve integrals of rational functions problems step by step online.

$\int\frac{8}{x^{13}}dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((8x^2)/(x^(3+2)^3))dx. Simplify the expression inside the integral. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. The integral of a function times a constant (8) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -13.

$-\frac{2}{3}x^{-12}+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int((8x^2)/(x^(3+2)^3))dx using partial fractionsSolve int((8x^2)/(x^(3+2)^3))dx using basic integralsSolve int((8x^2)/(x^(3+2)^3))dx using u-substitutionSolve int((8x^2)/(x^(3+2)^3))dx using integration by partsSolve int((8x^2)/(x^(3+2)^3))dx using trigonometric substitution

SnapXam A2

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9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main topic:

Integrals of Rational Functions

~ 0.07 s

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