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Solve the following integration int (...

Solve the following integration
`int (sin^(6)x+cos^(6)x)/(sin^(2) x * cos^(2)x)dx`

Text Solution

Verified by Experts

The correct Answer is:
`secx-"cosec"x+C`
`int(sin^(3)x+cos^(3)x)/(sin^(2)xcos^(2)x)dx=int(sin^(3)x)/(sin^(2)xcos^(2)x)dx+int(cos^(3)x)/(sin^(2)xcos^(2)x)dx`
`=int(sinx)/(cos^(2)x)dx+int(cosx)/(sin^(2)x)dx`
`=int tanxsecxdx+int cotx"cosec"xdx`
`=secx-"cosec"x+C`
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