`int(x sin^(-1))/(sqrt(1-x^(2)))` का मान ज्ञात कीजिए ।

Explanation

`int(x sin^(-1)x)/(sqrt(1-x^(2)))dx`
`=int(sin theta. theta)/(sqrt(1-sin^(2)theta)).cos theta d theta = int theta sin theta d theta`
`" "{:("माना "x=sin theta),(rArrdx=cos thetad theta):}`
`= theta sin theta d theta-int{(d)/(d theta)theta. int sin theta d theta}d theta`
(`theta` को प्रथम फलन लेने पर)
`=theta(-cos theta)-int1.(-cos theta)d theta`
`=- theta cos theta+int cos theta d theta`
`=- theta cos theta+sin theta+c`
`-theta sqrt(1-x^(2)theta)+sin theta+c`
`=x-sqrt(1-x^(2)).sin^(-1)x+c`