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int(sqrt(tanx))/(sinxcosx)dx is equal to...

`int(sqrt(tanx))/(sinxcosx)dx` is equal to.

A

`2sqrt(tanx)+C`

B

`2sqrt(cotx)+C`

C

`2sqrt(secx)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Dividing Nr and Dr by `cos^(2)x` we get
`I=int(sqrt(tanx))/(tanx)*sec^(2)xdx=int(sec^(2)x)/(sqrt(tanx))dx`
`=int(dt)/(sqrt(t))`, where tan x=t
`=2sqrt(t)+C=2sqrt(tanx)+C`.
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