∫e^x√{e^{2x} + 4}dx = ?

Question

\(\int{e^x}\sqrt{e^{2x}+4}\,dx\) = ?

∫e^x√{e^2x + 4}dx

A.\(\frac{1}2\)e^x\(\sqrt{e^{2x}+4}\) - 2 log |e^x + \(\sqrt{e^{2x}+4}\)| + c

B.\(\frac{1}2\)e^x\(\sqrt{e^{2x}+4}\) + 2 log |e^x + \(\sqrt{e^{2x}+4}\)| + c

C. e^x\(\sqrt{e^{2x}+4}\) + \(\frac{1}2\) log |e^x + \(\sqrt{e^{2x}+4}\)| + c

D. none of these

Answer 1

\(\int{e^x}\sqrt{e^{2x}+4}\,dx\)

Let e^x = t 

e^x dx = dt

= \(\int\sqrt{t^2+2^2}\,dt\)