ज्ञात करें `int (x tan^(-1)x)/((1+x^2)^("3/2"))dx`

Explanation

`z=tan^(-1)x` रखे तो `dz = 1/(1+x^2)dx` तथा `x =tan z`
अब, `I = int (z tan z )/sqrt(1+tan^2 z)dz = int z sin z dz`
`=z(-cos z) - int ( -cos z) dz = -z cos z + sin z +c`
`= - tan^(-1)x1/sqrt(1+x^2)+x/sqrt(1+x^2)+c`