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int (1)/(sqrt(sin^(3) x cos x))dx =?...

`int (1)/(sqrt(sin^(3) x cos x))dx =?`

A

`2sqrt(tanx)+C`

B

`2sqrt(cotx)+C`

C

`-2sqrt(tanx)+C`

D

`(-2)/(sqrt(tanx))+C`

Text Solution

Verified by Experts

The correct Answer is:
D
On dividing Nr and Dr by `cos^(2)x," we get "`
`I=int(sec^(2)x)/(sqrt(tan^(3)x))dx=int(dt)/(sqrt(t^(3)))`, where tan x=t.
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