Integral of (x2^(x^2))dx

∫ x * 2^(x^2) dx
=∫ x * e^(ln 2 * x^2) dx, let u=x^2, du = 2x dx
= ∫ 1/2 e^(ln 2 u) du
= 1/(2 ln 2) e^(ln 2 u) + C
= 1/(2 ln 2) 2^(x^2) + C