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Evaluate int tan^(2)x sin^(2)xdx...

Evaluate `int tan^(2)x sin^(2)xdx`

Text Solution

Verified by Experts

The correct Answer is:
`tanx-(3)/(2)x+(sin2x)/(4)+C`
`int tan^(2)x sin^(2)xdx=int(sin^(4)x)/(cos^(2)x)dx`
`=int(sin^(2)x(1-cos^(2)x))/(cos^(2)x)dx`
`=int(tan^(2)x-sin^(2)x)dx`
`=int(sec^(2)x-1-(1-cos2x)/(2))dx`
`=tanx-(3)/(2)x+(sin2x)/(4)+C`
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