Question

`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

Answer 1

Correct Answer - 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`