Question

Evaluate : `int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`

Answer 1

`int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`

`=int e^x[sin^-1x +1/ (sqrt(1-x^2))]dx`

We know that  `inte^x[f(x)+f'(x)]dx=e^x.f(x)+c`

`=e^x.sin^-1x+c`