Question

`int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx` is equal to
A. `log_(e)(tan^(2)x+sqrt(1+tan^(4)x))+C`
B. `(1)/(2)log_(e)(tan^(2)x+sqrt(1+tan^(4)x))+C`
C. `(1)/(4)log(tan^(2)x+sqrt(1+tan^(4)x))+C`
D. none of these

Answer 1

Correct Answer - b
Let `I=int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx`
`rArr I=int(tan xsec^(2)x)/(sqrt(tan^(4)x+1))dx=-(1)/(2)int(1)/(sqrt((tan^(2)x)^(2)+1))d(tan^(2)x)`
`rArrI=(1)/(2)log_(e){tan^(2)x+sqrt(1+tan^(4)x)}+C`