ज्ञात करें `int (sin x - cos x)/sqrt(sin 2 x )dx`

Explanation

`I = int (sin x-cos x)/sqrt(2 sin x cos x )dx = int (sin x-cos x)/sqrt(sin x +cos x)^2-1) dx`
यहां `sin x - cos x - sin x)` का `d.c. = - ( cos x + sin x)` का d.c. ]
`z=sin x + cos x` रखे, तो `dz = (cos x - sin x) dx`
अब `I = - int (dz) /sqrt(z^2-1)=-log |z+sqrt(z^2 -1)|+c`
`=-log |sinx +cos x+sqrt((sin x + cos x)^2-1)|+c`
` = -log | sin x + cos x + sqrt(cot x )+sqrt(tan x)) dx `