Find the antiderivatives.

Question

1. f(x)= x sin (x^2)

2. f(x)= x sin x

Answer 1

let u = x^2
du = 2x dx
and your integrand becomes
1/2 sin(u) du

for the 2nd one, use integration by parts

u = x
du = dx

dv = sin x dx
v = -cos x

∫u dv = uv - ∫v du
∫ x sinx dx = -x cos x + ∫cos x dx