Mathematics - Indefinite Integration Question with Solution | TestHub

$\int \frac{dx}{{\left(x+1\right)}^{\frac{3}{4}}{\left(x-2\right)}^{\frac{5}{4}}}$

$=\int \frac{dx}{{\left(x+1\right)}^2{\left(\frac{x-2}{x+1}\right)}^{\frac{5}{4}}}$

Put,$\frac{x-2}{x+1}=t$$\Rightarrow \frac{3}{{\left(x+1\right)}^2}dx=dt$

$\therefore I=\frac{-4}{3}\frac{1}{t^{\frac{1}{4}}}+c$

$=\frac{-4}{3}{\left(\frac{x+1}{x-2}\right)}^{\frac{1}{4}}+c$,$c$being the constant of integration.