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Find int(sin^6x)/(cos^8x)dxdot...

Find `int(sin^6x)/(cos^8x)dxdot`

A

`(tan^(6)x)/(6)+C`

B

`(tan^(7)x)/(7)+C`

C

`(tan^(8)x)/(8)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,`" "l=int(sin^(6)x)/(cos^(8)x)dx`
`l=int((sinx)/(cosx))^(6)((1)/(cos^(2)x))dx`
`l=int tan^(6)x sec^(2)xdx`
Put `tanx=t rArr sec^(2) x dx = dt`
`therefore" "l=int t^(6)dt rArr l=(t^(7))/(7)+C`
`l=(tan^(7)x)/(7)+C`
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