ज्ञात करें `int (sqrt(cot x) - sqrt( tan x)) dx`

Explanation

`I = sqrt2 int (cos x - sin x)/sqrt(2sin x cos x)dx" "[cos x - sin x = d.c. of ( sin x+cos x)]`
`=sqrt2 int (cosx -sinx)/sqrt((sin x +cos x)^(2)-1)dx = sqrt2 int (dz)/sqrt(z^(2)-1),` जहां `z=sin x + cos x `
`=sqrt2 log |z + sqrt( z^2 -1)+c`
`=sqrt2 log |sin x + cos x +sqrt(sin 2 x)| +c`