Question

find the integral t^5(t^6-7)^5 dt

Answer 1

\[\int{t^5(t^6-7)^5 dt}=\int{t^5(u)^5}dt\] \(u=t^6-7\) \(du=6t^5 dt\) \(\frac{du}{6}=t^5 dt\) \[\int{t^5(u)^5}dt=\frac{1}{6}\int{u^5}du=\frac{1}{6}(\frac{u^6}{6})=\frac{1}{6}*\frac{(t^6-7)^6}{6}+C\]

Answer 2

why did you put du/6?

Answer 3

Because \(\frac{du}{6}\)=\(\frac{1}{6}du\)

Answer 4

And im looking for a place which I can substitute : \((t^5 dt)\)