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Evaluate: inte^sin^((-1)x)dxdot...

Evaluate: `inte^sin^((-1)x)dxdot`

Text Solution

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Let `sin^(-1)x=t implies x=sint impliesdx=cos t dt`
` :. I=int e^(sin^(-1)x)dx`
`=int e^(t)cost dt`
`=(e^(t))/(2)(sint+cost)+c`
`=(e^(sin^(-1)x))/(2)(x+sqrt(1-x^(2)))+c`
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