1.

Integrate the following functions x tan^-1x

Answer»

SOLUTION :`int x tan^-1x DX`
=`tan^-1x xx x^2/2 - int 1/(1+x^2) x^2/2 dx`
=`x^2/2 tan^-1 x- 1/2 int (1+x^2-1)/(1+x^2) dx`
`x^2/2 tan^-1 x-1/2 int (1-1/(1+x^2)) dx`
=`x^2/2 tan^-1 x- 1/2(x-tan^-1 x)+C`
=`x^2/2 tan^-1 -x/2 +1/2 tan^-1 x+c`


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