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intcos^(-3//7)xsin^(-11//7)xdx is equal ...

`intcos^(-3//7)xsin^(-11//7)xdx` is equal to

A

`log|sin^(4//7)x|+c`

B

`(4)/(7)tan^(4//7)x+c`

C

`-(7)/(4)tan^(-4//7)x+c`

D

`log|cos^(3//7)x|+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`intcos^(-3//7)xsin^(-11//7)xdx`
`=int(sin^(-11//7)x)/(cos^(-11//7)x)*sec^(2)xdx`
`=int tan^(-11//7)xsec^(2)xdx`
Put tan x=t
`implies sec^(2)xdx=dt`
`thereforel=int t^(-11//7)dt`
`=-(7)/(4)tan^(-4//7)x+c`
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