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Evaluate : int(sin2x)/(a^2+b^2sin^2x)dx...

Evaluate : `int(sin2x)/(a^2+b^2sin^2x)dx`

Text Solution

Verified by Experts

Assume, `a^2 + b^2sin^2x = t`
`d(a^2 + b^2sin^2x) = dt`
`2b^2.sinx.cosx.dx = dt`
`(2sinx.cosx = sin2x) `
`Sin2x dx = dt/b^2`
Put t and dt in the given equation we get
⇒`1/b^2 ∫dt/t `
=`1/b^2 ln|t| + c `
=`1/b^2 ln|a^2 + b^2sin^2x| + c.`
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