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

Explanation

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

I= `int1/(sqrt(1-x^2)sqrt(9+(sin^(-1)x)^2)\ dx`

Let `sin^(-1)x=t`

=`1/sqrt(1-x^2)dx=dt`

I=`int dt/sqrt(9+t^2)`

=`log(​t+sqrt(t^2+9))
​​+C`

=`log(​sin^(-1)x+sqrt((sin^(-1)x)^2+9))
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