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Find the integral $\int x^2\left(x+2\right)^2dx$

Step-by-step Solution

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Final Answer

$\frac{x^{5}}{5}+x^{4}+\frac{4}{3}x^{3}+C_0$
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Step-by-step Solution

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Rewrite the integrand $x^2\left(x+2\right)^2$ in expanded form

$\int\left(x^{4}+4x^{3}+4x^2\right)dx$

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$\int\left(x^{4}+4x^{3}+4x^2\right)dx$

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Learn how to solve integral calculus problems step by step online. Find the integral int(x^2(x+2)^2)dx. Rewrite the integrand x^2\left(x+2\right)^2 in expanded form. Expand the integral \int\left(x^{4}+4x^{3}+4x^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{4}dx results in: \frac{x^{5}}{5}. The integral \int4x^{3}dx results in: x^{4}.

Final Answer

$\frac{x^{5}}{5}+x^{4}+\frac{4}{3}x^{3}+C_0$

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 integral of x^2(x+2)^2dx using partial fractionsSolve integral of x^2(x+2)^2dx using basic integralsSolve integral of x^2(x+2)^2dx using u-substitutionSolve integral of x^2(x+2)^2dx using integration by partsSolve integral of x^2(x+2)^2dx using trigonometric substitution

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Function Plot

Plotting: $\frac{x^{5}}{5}+x^{4}+\frac{4}{3}x^{3}+C_0$

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1
2
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4
5
6
7
8
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

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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