1.

If C is arbitrary constant then inte^(sin^(-1)x)((lnx)/(sqrt(1-x^(2)))+1/x)dx is equal to

Answer»

`e^(SIN^(-1)xcosx)+C`
`-esin^(-1)x.ln(1/x)+C`
`(e^(sin^(-1)x))/x+C`
`e^(sin^(-1)x)/(sin^(-1)x)+C`

Solution :`inte^(sin-1)x((lnx)/(sqrt(1-x^(2)))+1/x)dx`
PUT `x=sin theta impliesdx=cos theta d theta`
`inte^(theta)((ln sin theta)/(cos theta)+1/(sin theta))cos theta d theta`
`=inte^(theta)(ln sin theta+cot theta)d theta=e^(0).ln(sin theta)+c`
`=e^(sin^(-1)x) lnx+c=-e^(sin^(-1)In(1/x)+C`


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