Question

`int("cosec x")/(cos^(2)(1+log tan.(x)/(2)))dx` is equal to
A. `sin^(2)[1+log tan.(x)/(2)]+C`
B. `tan[1+log tan.(x)/(2)]+C`
C. `sec^(2)[1+log tan.(x)/(2)]+C`
D. `-tan[1+log tan.(x)/(2)]+C`

Answer 1

Correct Answer - B
Let `l=int("cosec x")/(cos^(2)(1+log tan.(x)/(2)))dx`
Put `1+log tan.(x)/(2)=t`
`rArr (1)/(tan.(x)/(2)).sec^(2).(x)/(2).(1)/(2)dx=dt rArr" cosec x dx = dt "` ltBrgt `therefore" "l=int(dt)/(cos^(2)t)=int sec^(2)t dx=tant+C`
`=tan(1+log tan.(x)/(2))+C`