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int(In(tanx))/(sinx cosx)dx " is equal t...

`int(In(tanx))/(sinx cosx)dx " is equal to "`

A

`(1)/(2)In(tanx)+c`

B

`(1)/(2)In(tan^(2)x)+c`

C

`(1)/(2)(In(tanx))^(2)+c`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(In(tanx))/(sinx cosx)dx`
`"Let " t=In(tanx)`
`"or " (dt)/(dx)=(sec^(2)x)/(tanx)`
`"or " dt=(dx)/(sinx cosx)`
`:. I=int tdt=(1)/(2)t^(2)+C=(1)/(2)(In(tanx))^(2)+C`
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