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Evaluate: int(x^2sin^(-1)x)/((1-x^2)^(3s...

Evaluate: `int(x^2sin^(-1)x)/((1-x^2)^(3setminus2))\ dx`

Text Solution

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Let `I=int frac{x^{2} sin ^{-1} x}{(1-x^{2})^{3 / 2}}`
` sin ^{-1} x=t `
` frac{1}{sqrt{1-x^{2}}} d x=d t `
` I=int frac{sin ^{2} t times t d t}{1-sin ^{2} t} `
` =int frac{sin ^{2} t}{cos ^{2} t} d t `
` =int tan ^{2} t d t `
` =int t(sec ^{2} t-1) d t`
...
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