<s>[INST] Integration problem: $\int x^{2} -x 4^{-x^{2}} dx$ I need to integrate $$\int x^{2} -x 4^{-x^{2}} dx$$ 
and I know the answer I got is wrong. However, I can't figure out where I went wrong. These steps I took:

Appreciate any help!
 [/INST] $$\begin{align}
\int x^{2} - x4^{-x^{2}} dx &= \int x^{2} dx - \int x4^{-x^{2}} dx \\
&= \frac{x^{3}}{3} + \int -x4^{-x^{2}} dx \\
\end{align}$$
notice that 
$$\frac{d}{dx} 4^{-x^{2}} = -2x\cdot \ln4 \cdot 4^{-x^{2}}$$
So if 
$$\begin{align}
u &= 4^{-x^{2}} \\
\implies du &= -2x\cdot \ln4 \cdot 4^{-x^{2}} dx \\
\implies \frac{du}{2 \ln4} &= -x 4^{-x^{2}} dx
\end{align}$$
So our integral becomes
$$\begin{align}
\frac{x^{3}}{3} + \int -x4^{-x^{2}} dx &= \frac{x^{3}}{3} + \int \frac{du}{2 \ln4} \\
&= \frac{x^{3}}{3} + \frac{u}{2 \ln4} + C \\
&= \frac{x^{3}}{3} + \frac{4^{-x^{2}}}{2 \ln4} + C \\
\end{align}$$
</s>