# Evaluate the integral: {eq}\displaystyle \int x^2\ tan^{-1}\ x\ dx {/eq}

## Question:

Evaluate the integral:

{eq}\displaystyle \int x^2\ tan^{-1}\ x\ dx {/eq}

## Integration by Parts:

The method of finding the integral of the composition of two functions when they are in the product by taking them function one and function second is known as the integration by parts. The integration by parts formula is given below

$$\int\left(u\cdotp v\right)\text{ d}x=u\int v\text{ d}x-\int\left(\dfrac{\text{ d}}{\text{ d}x}u\int v\text{ d}x\right)\text{ d}x$$

\begin{align} I&=\int x^{2}\arctan(x)\text{ d}x\\[0.3cm] I&=\arctan(x)\int x^{2}\text{ d}x-\int\left(\dfrac{\text{ d}}{\text{...