Question

how do I solve the integral 2/(e^(2x)+4) ? using the substitution u=e^(2x)+4

Answer 1

\[\int\frac{2}{e^{2x}+4}dx\]
\[u=e^x\\du=e^x\;dx\\
\frac{1}{e^x}du=dx\\
\frac{1}{u}du=dx\]
\[2\int\frac{1}{u^2+4}\left(\frac{1}{u}du\right)\\
2\int\frac{1}{u(u^2+4)}du\]
Partial fraction decomposition?

Answer 2

\[\Large \frac{2}{e^{2x}+4}\cdot\frac{e^{-2x}}{e^{-2x}}=\frac{2e^{-2x}}{1+4e^{-2x}}\]

Answer 3

Oh, sorry. Didn't notice the substitution requirement.

Answer 4

it can also be solved by partial fraction.