Evaluate ∫$$1(x$$−$$3)x+1dx$$

Correct option is 112log⁡x+1−2x+1+2+C

Questions

$Evaluate \int \frac{1}{(x - 3) \sqrt{x + 1}} d x$

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12log⁡x+1−2x+1+2+C

12log⁡x+1+2x+1-2+C

14log⁡x+1−2x+1+2+C

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detailed solution

Correct option is A

Let I=∫1(x−3)x+1dx Let x+1=t2 or dx=2tdt ∴ I=∫1t2−1−32tt2dt=2∫dtt2−22=2×12(2)log⁡t−2t+2+C=12log⁡x+1−2x+1+2+C

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Evaluate ∫1(x−3)x+1dx

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$Evaluate \int \frac{1}{(x - 3) \sqrt{x + 1}} d x$