Answer
$\int x2^{x^{2}}dx=\frac{1}{2}\frac {2^{x^{2}}}{ln2}+constant$
Work Step by Step
Evaluate the integral $\int x2^{x^{2}}dx$
Consider $x^{2}=t$ and $xdx=\frac{dt}{2}$
Thus, $\int x2^{x^{2}}dx=\int 2^{t}\frac{dt}{2}$
$=\frac{1}{2}\frac{2^{t}}{ln2}+constant$
Hence, $\int x2^{x^{2}}dx=\frac{1}{2}\frac {2^{x^{2}}}{ln2}+constant$
