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$\int \frac{1}{{[(x - 1)^{3} (x + 2)^{5}]}^{1 / 4}} dx$ is equal to

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43x−1x+21/4+C

43x+2x−11/4+C

13x−1x+21/4+C

13x+2x−11/4+C

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detailed solution

Correct option is A

∫1(x−1)3(x+2)51/4dx=∫1x−1x+23/4(x+2)2dx=13∫1t3/4dt put x−1x+2=t⇒3(x+2)2dx=dt=13t1/414+C=43t1/4+C=43x−1x+21/4+C

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∫1(x−1)3(x+2)51/4dx is equal to

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$\int \frac{1}{{[(x - 1)^{3} (x + 2)^{5}]}^{1 / 4}} dx$ is equal to