Answer
$\frac{3^{{x^2}}}{2\ln 3} +c $
Work Step by Step
Let $ u=3^{x^2}$, then $ du= 2x3^x \ln 3 dx $ and hence
$$\int x3^{x^2}dx = \frac{1}{2\ln 3}\int du +c=\frac{1}{2\ln 3}u +c\\
=\frac{1}{2\ln 3}3^{x^2} +c =\frac{3^{{x^2}}}{2\ln 3} +c. $$
