If `int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c,` then

Options

A. `(-2)/(sqrt(tanx))+(2)/(3)(tanx)^(3//2)+C`
B. `(2)/(sqrt(tanx))(2)/(3)(tanx)^(3//2)+C`
C. `(-2)/(sqrt(tanx))+(2)/(3)(tanx)^(1//3)+C`
D. none of these

Answer

a

Explanation

`I=int(1)/(sqrt(sin^(3)xcos^(5)x))dx`
`rArrI=int(1)/(sin^(3//2)x cos ^(5//2)x)dx`
`rArr I=int(sec^(4)x)/(tan^(3//2)x)dx` " " `["Dividing"N^(r)and^(r) "by" cos^(2)x]`
`rArrI=int((1+tan^(2)x))/(tan^(3//2)x)d (tanx)`
`rArr I=int{(tanx)^(-3//2)+(tanx)^(1//2)}d (tanx)`
`rArr I=-2(tanx)^(-1//2)+(2)/(3)(tanx)^(3//2)+C`
`rArrI=(-2)/(sqrt(tanx))+(2)/(3)(tanx)^(3//2)+C`