Evaluate: `inte^xdot(sqrt(1-x^2)sin^(-1)x+1)/(sqrt(1-x^2))\ dx`

Explanation

Given, `int e^(x) [(sqrt(1-x^(2))sin^(-1) x +1)/(sqrt(1-x^(2)))]dx`
Let ` I = inte^(x) [(sqrt(1-x^(2))sin^(-1)x+1)/(sqrt(1-x^(2)))]dx`
` = int e^(x) [sin^(-1) x + 1/sqrt(1-x^(2))]dx`
Put ` f(x) = sin^(-1) x `
` f'(x) = 1/(sqrt(1-x^(2)))`
We know that
`int e^(x) [f(x)+f'(x)'*dx = e^(x) f(x)+c].`
so ` I = e^(x) sin^(-1) x + c`