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Evaluate: int1/(sqrt((1-x^2){9+(sin^(-1)...

Evaluate: `int1/(sqrt((1-x^2){9+(sin^(-1)x)^2}))\ dx`

Text Solution

Verified by Experts

I=`int1/(sqrt((1-x^2){9+(sin^(-1)x)^2}))\ dx`
Let `sin^(−1)x=t`
`(dx)/(sqrt(1-x^2))dx=dt`
`I=int (dt)/(sqrt(9+t^2))`
`I=log∣​t+sqrt(t^2+9)∣​+C`
`I=log∣sin^(−1)x+sqrt((sin^(−1)x)^2+9 )​∣​+C`
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