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

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?

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

1 Answer 1

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

$$\int \cfrac{\cfrac{11}{x^{12}} - \cfrac{18}{x^{13}}}{\sqrt[6]{1+\cfrac{-2}{x^{11}}+\cfrac{3}{x^{12}}}}$$

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  • $\begingroup$ good observation! Problem seems to be specifically made to be solved in this manner. $\endgroup$
    – King Tut
    Apr 3, 2018 at 10:32
  • $\begingroup$ @Kumar Ayush..........super observation.... $\endgroup$ Apr 3, 2018 at 10:41
  • $\begingroup$ @KingTut yeah i also think so $\endgroup$
    – kayush
    Apr 3, 2018 at 10:45

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