Question

If ∫sin^-1 √(x/(1 + x) dx = A(x) tan^-1(√x) + B(x) + C, where C is a constant of integration, then the ordered pair (A(x), B(x)) can be :

(1) (x - 1, √x)

(2) (x + 1, √x)

(3) (x + 1, -√x)

(4) (x - 1, - √x)

Answer 1

(3) (x + 1, -√x)