# Find the integral $\int \frac{11x-18}{x^{11} \sqrt[6]{x^{12}-2x+3}}dx$

$$\int \frac{11x-18}{x^{11} \sqrt[6]{x^{12}-2x+3}}dx$$

I am trying to solve using $$x^{12}-2x+3=t \implies (12x^{11}-2)dx=dt$$

I am facing the problems, can anyone help me?

• @ SmarthBansal..what is maximum method
– user543273
Apr 3, 2018 at 10:18

Hint: Just take $x^{12}$ out from radical, Denominator becomes $x^{13} {\sqrt[6]{1+\cfrac{-2}{x^{11}}+\cfrac{3}{x^{12}}}}$:
$$\int \cfrac{\cfrac{11}{x^{12}} - \cfrac{18}{x^{13}}}{\sqrt[6]{1+\cfrac{-2}{x^{11}}+\cfrac{3}{x^{12}}}}$$