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Evaluate int sin^4x/(cos^8x)dx...

Evaluate `int sin^4x/(cos^8x)dx`

Text Solution

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we have, `l=int(sin^(4)x)/(cos^(8)x)dx`
Dividing numerator and denominator by `cos^(4)x`
`l=int(tan^(4)x)/(cos^(4)x)dximpliesl=inttan^(4)xsec^(4)xdx`
`:.l=inttan^(4)x{1+tan^(2)x}sec^(2)xdx`, put `tanx=t`
`:.l=intt^(4)(1+t^(2))dtimpliesl=int(t^(4)+t^(6))dt`
`:.l=(t^(5))/(5)+(t^(7))/(7)+Cimpliesl=(tan^(5)x)/(5)+(tan^(7)x)/(7)+C`
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