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Evaluate the following integrals: int(...

Evaluate the following integrals:
`int(sin^(-1)x)/(x^(2))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(-sin^(1)x)/(x)+log|(1)/(x)-(sqrt(1-x^(2)))/(x)|+C`
Put x=sin t and dx=cos t dt. Then,
`I=intt("cosec"cott)dt=-"cosec"+log|"cosec "t-cott|+C`
`=(-sin^(-1)x)/(x)+log|(1)/(x)-(sqrt(1-x^(2)))/(x)|+C`.
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