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

## Step-by-step Solution

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###  Videos

$-x^2\cos\left(x\right)+2x\sin\left(x\right)+2\cos\left(x\right)+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int x^2\sin\left(x\right)dx$

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We can solve the integral $\int x^2\sin\left(x\right)dx$ by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form $\int P(x)T(x) dx$. $P(x)$ is typically a polynomial function and $T(x)$ is a transcendent function such as $\sin(x)$, $\cos(x)$ and $e^x$. The first step is to choose functions $P(x)$ and $T(x)$

$\begin{matrix}P(x)=x^2 \\ T(x)=\sin\left(x\right)\end{matrix}$

Learn how to solve integral calculus problems step by step online.

$\begin{matrix}P(x)=x^2 \\ T(x)=\sin\left(x\right)\end{matrix}$

Learn how to solve integral calculus problems step by step online. Find the integral int(x^2sin(x))dx. We can solve the integral \int x^2\sin\left(x\right)dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x), so we must integrate \sin\left(x\right) a total of 3 times. With the derivatives and integrals of both functions we build the following table.

$-x^2\cos\left(x\right)+2x\sin\left(x\right)+2\cos\left(x\right)+C_0$

##  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^2sinxdx using basic integralsSolve integral of x^2sinxdx using u-substitutionSolve integral of x^2sinxdx using integration by partsSolve integral of x^2sinxdx using tabular integration

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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

### Main topic:

Integral Calculus

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