Find the integral using the indicated substitution. ,

Name: Find the integral using the indicated substitution. ,
Brand: Quizplus
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Question

Find the integral using the indicated substitution.  ,

Quizplus · Accepted Answer

The given integral is in the form of $\int e^x\sqrt{e^{2x}-1}dx$. By substituting $u=e^x$ we get $du=e^x dx$ and $\sqrt{e^{2x}-1}=\sqrt{u^2-1}$.
So, the integral becomes $\int \sqrt{u^2-1}du$ which can be solved by the substitution $u=\sec	heta$. 
Therefore, the correct choice is (D).

Find the Integral Using the Indicated Substitution