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

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

Text Solution

Verified by Experts

`(d)/(dx)(a^(2)sin^(2)x+b^(2)cos^(2)x)=(a^(2)-b^(2))sin2x`
Now, `int(sin2x)/(a^(2)sin^(2)x+b^(2)cos^(2)x)dx`
`=(1)/((a^(2)-b^(2)))int((a^(2)-b^(2))sin2x)/(a^(2)sin^(2)x+b^(2)cos^(2)x)dx`
`=(1)/((a^(2)-b^(2)))int((d)/(dx)(a^(2)sin^(2)x+b^(2)cos^(2)x))/(a^(2)sin^(2)x+b^(2)cos^(2)x)dx`
`=(1)/((a^(2)-b^(2)))log|a^(2)sin^(2)x+b^(2)cos^(2)x|+C`
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