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int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx is...

`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

Text Solution

Verified by Experts

The correct Answer is:
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`
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