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Evaluate: int1/(sqrt(1-x^2)(2+3sin^(-1)...

Evaluate: `int1/(sqrt(1-x^2)(2+3sin^(-1)x)))dx`

Text Solution

Verified by Experts

We have given,
`int1/(sqrt(1-x^2)(2+3sin^(-1)x)))dx`
Let `t=2+3sin^-1x`
`dt=3/sqrt(1-x^2)dx`
`dt=3(dx/sqrt(1-x^2))`
`I=int1/(sqrt(1-x^2)(2+3sin^(-1)x)))dx=(1/3)int(dt)/t`
`I=(1/3)log∣t∣+c`
...
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