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Evaluate: (i) int((sin^(-1)x)^3)/(sqrt(1...

Evaluate: (i) `int((sin^(-1)x)^3)/(sqrt(1-x^2))\ dx` (ii) `int(sin(2+3logx)/x\ dx`

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(i) `int frac{(sin ^{-1} x)^{3}}{sqrt{1-x^{2}}} d x `
`text { Let } sin ^{-1} x=t `
`Rightarrow frac{1}{sqrt{1-x^{2}}} d x=d t `
`text { Now, } int frac{(sin ^{-1} x)^{3}}{sqrt{1-x^{2}}} d x `
`=int t^{3} d t `
`=frac{t^{4}}{4}+C `
`=frac{(sin ^{-1} x)^{4}}{4}+C`

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