Mathematics - Indefinite Integration Question with Solution | TestHub

$\Rightarrow \int {\left(\frac{x-3}{x+4}\right)}^{\frac{-6}{7}}\frac{1}{{\left(x+4\right)}^2}dx ...\left(\mathrm{i}\right)$

Let $\frac{x-3}{x+4}=t^7$ ,

$\frac{7}{{\left(x+4\right)}^2}dx=7t^{6}dt ... \left(\mathrm{ii}\right)$

From $\left(\mathrm{i}\right)$ from $\left(\mathrm{ii}\right)$,

$\int t^{-6}{t}^{6}dt=t+C$