Step-by-step Solution

Integrate $x^2\sin\left(x\right)$ with respect to x

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Step-by-step explanation

Problem to solve:

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

Learn how to solve calculus problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve calculus problems step by step online. Calculate the integral of x^2sin(x). 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). With the derivatives and integrals of both functions we build the following table.

Final Answer

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

Main topic:

Calculus

Related formulas:

4. See formulas

Time to solve it:

~ 0.03 s (SnapXam)