Answer
$$\int x3^{x^2}dx=\frac{3^{x^2}}{2\ln3}+C$$
Work Step by Step
$$A=\int x3^{x^2}dx$$
We set $a=x^2$, which means $$da=2xdx$$ $$xdx=\frac{1}{2}da$$
Therefore, $$A=\frac{1}{2}\int3^ada$$ $$A=\frac{1}{2}\times\frac{3^a}{\ln3}+C$$ $$A=\frac{3^a}{2\ln3}+C$$ $$A=\frac{3^{x^2}}{2\ln3}+C$$
