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Question

Question: \(\int_{0}^{\log_{e}5}\frac{e^{x}\sqrt{e^{x}–1}}{e^{x} + 3}\) dx =...

∫0log⁡e5exex–1ex+3\int_{0}^{\log_{e}5}\frac{e^{x}\sqrt{e^{x}–1}}{e^{x} + 3} dx =

A

3 + 2p

B

4 – p

C

2 + p

D

4 + p

Answer

4 – p

Explanation

Solution

Put ex – 1 = t2

Ž ex dx = 2tdt

Ž I = ∫02t.2tdtt2+4\int_{0}^{2}\frac{t.2tdt}{t^{2} + 4}