Evaluate: `inttan^(-1)xdx` .

Explanation

`int tan ^{-1} x cdot d x`
`
=int tan ^{-1} x cdot int tan ^{-1} d x+c`

Apply Rule of integration by parts by taking `tan ^{-1} x` as the first function.


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