∫x−$$3(x$$−$$1)3$$⋅exdx is equal to

Correct option is 4ex(x−1)2+C

Questions

$\int \frac{x - 3}{(x - 1)^{3}} \cdot e^{x} dx$ is equal to

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ex(x−1)+c

−ex(x−1)2+C

2ex(1−x)2+C

ex(x−1)2+C

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detailed solution

Correct option is D

Let I=∫x−3(x−1)3exdx=∫x−1−2(x−1)3exdx=∫exx−1(x−1)3−2(x−1)3dx=∫ex1(x−1)2−2(x−1)3dxLet f(x)=1(x−1)2⇒f′(x)=−2(x−1)3 ∴ I=ex(x−1)2+C ∵∫exf(x)+f′(x)dx=exf(x)

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∫x−3(x−1)3⋅exdx is equal to

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$\int \frac{x - 3}{(x - 1)^{3}} \cdot e^{x} dx$ is equal to