Evaluate: `intx^2tan^(-1)x\ dx`

Explanation

`int {x}^{2} tan ^{-1} x d x`
`
=tan ^{-1} x int x^{2} d x-int frac{1}{1+x^{2}} cdot frac{x^{3}}{3} d x`
`
=frac{x^{3}}{3} tan ^{-1} x-frac{1}{3} int(x-frac{x}{1+x^{2}}) d x`
`
=frac{x^{3}}{3} tan ^{-1} x-frac{x^{2}}{6}+frac{1}{6} log |1+x^{2}|+C`
`