Question

`int(1)/(1+3 sin ^(2)x)dx` is equal to
A. `(1)/(3)tan^(-1)(3 tan^(2)x)+C`
B. `(1)/(2)tan^(-1)(2tan x)+C`
C. `tan^(-1) (tanx)+C`
D. none of these

Answer 1

Correct Answer - b
We have , `I=int(1)/(1+3 sin^(2)x)dx = int(sec^(2)x)/(sec^(2)x+3tan^(2)x)dx`
`rArr I=(1)/(2)int(1)/((2 tan x)^(2)+1^(2))d (2 tanx)`
`rArr I=(1)/(2)tan^(-1)(2tanx)+C`