2-x-1-x-1-4-dx-

Question Number 191188 by cortano12 last updated on 20/Apr/23

\int \sqrt[4]{\frac{2 - x}{1 - x}} dx = ?

Answered by mehdee42 last updated on 20/Apr/23

\sqrt[4]{\frac{2 - x}{1 - x}} = u \Rightarrow x = \frac{u^{4} - 2}{u^{4} - 1} \Rightarrow d x = \frac{4 u^{3}}{{(u^{4} - 1)}^{2}} d u

\Rightarrow \int \sqrt[4]{\frac{x - 2}{x - 1}} d x = \int \frac{4 u^{4}}{{(u^{4} - 1)}^{2}} d u

t h i s i n t e g r a l c a n b e s o l v e d b y d i v i d i n g f r a c t i o n s .

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