Compute $\int \big( (4z)^5 + 4(4z)^2 \big ) \big( (4z)^3 +1 \big)^{12} dz$ by substitution The problem is $\int \big( (4z)^5 + 4(4z)^2 \big ) \big( (4z)^3 +1 \big)^{12} dz$. I know a substitution has to be used, but having the $4$ in front of the $4z$ is confusing me and I don't know how to get rid of it. 

\begin{align}
&(4z \mapsto y)\\
&\int \left((4z)^5+4(4z)^2\right)\left((4z)^3+1\right)^{12}dz\\
&=\frac14\int y^2\left(y^3+4\right)\left(y^3+1\right)^{12}dy\\
&\\
&(y^3\mapsto x)\\
&=\frac1{12}\int (x+4)(x+1)^{12}dx\\
&=\frac1{12}\int (x+1)(x+1)^{12}dx+\frac1{12}\int 3(x+1)^{12}dx\\
&=\frac1{12\cdot14}(x+1)^{14}+\frac1{4\cdot13}(x+1)^{13}\\
&=\frac1{12\cdot14}(\sqrt[3]{4z}+1)^{14}+\frac1{4\cdot13}(\sqrt[3]{4z}+1)^{13}\\
\end{align}
