`tan^(-1)x`

Explanation

`int tan^(-1)xdx`
`=int tan^(-1)x.1dx`
`=tan^(-1)x. int 1dx - int{(d)/(dx)tan%(-1)x. int 1dx}dx`
( `tan^(-1) x` को प्रथम लेने पर )
`=x tan^(-1)x-int(x)/(1+x^(2))dx" माना "1+x^(2)=t`
`=x tan^(-1)x-int(dt)/(2t)" "therefore " "2x=(dt)/(dx)`
`=x tan^(-1)x-(1)/(2)logt+C" "rArr" "xdx=(dt)/(2)`
`=x tan^(-1)x-(1)/(2)log(1+x^(2))+C`