Correct option is 12ex-1 -tan-1ex-1 +c

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$\int \sqrt{e^{x} - 1} d x =$

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2ex-1 -tan-1ex-1 +c

ex-1 -tan-1ex-1 +c

ex-1 +tan-1ex-1 +c

2ex-1 +tan-1ex-1 +c

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detailed solution

Correct option is A

Let I=∫ex−1 dxPut ex−1=t2 ⇒exdx=2t dt⇒ dx=2t1+t2dtI=∫t.2t1+t2dt = ∫ 2t21+t2dt =∫2t2+2−21+t2dt =2∫t2+11+t2dt−2∫11+t2dt =2t−2tan−1t+c =2ex−1 −tan−1ex−1 +c

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∫ex-1 dx =

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$\int \sqrt{e^{x} - 1} d x =$