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

Explanation

We have given `int x^2 tan^(-1)x\ dx`

`I=int x^2 tan^(-1)x\ dx`

By integration by parts

`I=tan^(-1)int x^2dx-int [(d/(dx)tan^(-1)x)int x^2dx]dx`

`I=tan^(-1)x((x^3)/3)-int1/(1+x^2).(x^3)/3dx`

`I=((x^3)/3)tan^(-1)x-int1/(1+x^2).(x^3)/3dx`

`I=((x^3)/3)tan^(-1)x-(1/3)int(x^3)/(1+x^2)dx`

Let `1+x^2=t implies 2dx=dt implies dx=(dt)/(2x)`

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