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Evaluate: int(sinx)/(sin4x)dx...

Evaluate: `int(sinx)/(sin4x)dx`

Text Solution

Verified by Experts

Given
`int(sinx)/(sin4x)dx`
Let
`I=int(sinx)/(sin4x)dx`
`I=(1/4)int(1)/(cosx(cos^2x-sin^2x)))dx`
`I=(1/4)int(cosx)/(cosx(cos^2x-sin^2x)))dx`
Put `sinx=t⇒cosxdx=dt`
`I=(1/4)int(dt)/((1-t^2)(1+t^2))dx`
...
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