How to integrate $\int \frac 1 {\begin{pmatrix}\frac1 3 t - 8\end{pmatrix}^5} \,dt$ by substitution? I am required to solve this question via integration by an appropriate substitution. This is the first time I am doing it with no help on the substitution part. Hence, could somebody help me check this working?
$$
\begin{align*}
\int \frac 1 {\begin{pmatrix}\frac1 3 t - 8\end{pmatrix}^5} \,dt
= 3\int \frac 1 {\begin{pmatrix}\frac1 3 t - 8\end{pmatrix}^5} \,\frac 1 3dt
\end{align*}
$$
Consider the substitution $u = \begin{pmatrix}\frac 1 3 t -8\end{pmatrix}$ and so $du = \frac 1 3 dt$ and perform the substitution
$$
\begin{align*}
3\int \frac 1 {\begin{pmatrix}\frac1 3 t - 8\end{pmatrix}^5} \,\frac 1 3dt
&= 3\int\frac 1 {u^5} \, du
\\&= -\frac 3 4 u^{-4} + C
\\&= -\frac 3 4 \begin{pmatrix}\frac 1 3 t -8\end{pmatrix}^{-4} +C
\end{align*}
$$

Thank you to all who have helped, my proposed solution has been verified and is correct.
