∫x−1x+234x+22dxPut x−1x+2=t

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$\int \frac{1}{\sqrt[4]{{(x - 1)}^{3} {(x + 2)}^{5}}} d x =$

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$\frac{3}{4} {(\frac{x + 2}{x - 1})}^{\frac{3}{4}} + c$

$\frac{3}{4} {(\frac{x + 2}{x - 1})}^{\frac{1}{4}} + c$

$\frac{4}{3} {(\frac{x - 1}{x + 2})}^{\frac{5}{4}} + c$

$\frac{4}{3} {(\frac{x - 1}{x + 2})}^{\frac{1}{4}} + c$

answer is A.

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Detailed Solution

$\int \frac{{(\frac{x - 1}{x + 2})}^{\frac{3}{4}}}{{(x + 2)}^{2}} d x$

Put $\frac{x - 1}{x + 2} = t$

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