# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve trigonometric integrals problems step by step online.

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

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(x^2*sin(2*x))dx. We can solve the integral \int x^2\sin\left(2x\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.

$-\frac{1}{2}x^2\cos\left(2x\right)+\frac{1}{2}x\sin\left(2x\right)+\frac{1}{4}\cos\left(2x\right)+C_0$

### Problem Analysis

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

### Main topic:

Trigonometric integrals

~ 0.09 seconds