<s>[INST] Expanding an Integrand I am trying to solve this integral but it looks like I do not get the right result. Can you please help me?
$$\int{(t-4)(t+2)^{\frac 4 5}}dt$$
I set $u=t+2$, so I get $\int{(u-6)u^{\frac 4 5}} \Bbb d t$ and then the solution I get is $$\frac 5 {14} (t+2)^{\frac {14} 5}-\frac{10} 3 (t+2)^{\frac 9 5} .$$
Can you please tell me where I am wrong?
 [/INST] $$\begin{align}
\int{(t-4)(t+2)^{\frac {4}{5}}}dt
&=\int({t(t+2)^{\frac {4}{5}}-4(t+2)^{4/5}})dt\\
&=\int{t(t+2)^{\frac {4}{5}}}dt-4\int{(t+2)^{4/5}}dt\\
\end{align}$$
Subtitute $u=t+2$ and $du=dt$
$$\begin{align}
&=\int{(u-2)u^{4/5}}du-4\int{(t+2)^{4/5}}dt\\
&=\int{(u^{9/5}-2u^{4/5}})du-4\int{(t+2)^{4/5}}dt\\
&=\int{u^{9/5}}du-2\int{u^{4/5}}du-4\int{(t+2)^{4/5}}dt\\
&=\frac{5}{42}(t+2)^{9/5}(3t-22)+c
\end{align}
$$
</s>