Question

Integrate the expression below

Answer 1

$\displaystyle\int~4t(5t^2-1)^6 dt \\\\[-0.35em] ~\dotfill\\\\ u=5t^2-1\implies \cfrac{du}{dt}=10t~\hspace{10em} \cfrac{du}{10t}=dt \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~4t~u^6\cdot \cfrac{du}{10t}\implies \int~\cfrac{4t~u^6}{10t}\cdot du\implies \int~\cfrac{2~u^6}{5}du\implies \cfrac{2}{5}\int~u^6\cdot du \\\\\\ \cfrac{2}{5}\cdot \cfrac{u^7}{7}\implies \cfrac{2(5t^2-1)^7}{35}$