Question

\(\int(t^9\sqrt[4]{t^5+1})dt\)

I hate this stuff , what is the best rout?

Answer 1

Set \(\color{blue}{u=t^5+1}\), so \(\color{red}{du=t^4~dt}\). You also have \(\color{green}{u-1=t^5}\).
\[\int t^9\sqrt[4]{t^5+1}~dt=\int \color{green}{t^5} \color{red}{t^4}\sqrt[4]{\color{blue}{t^5+1}}~\color{red}{dt}\]

Answer 2

Pff you know I meant \(\color{red}{\dfrac{1}{5}du=t^4~dt}\).

Answer 3

You're welcome!