Integral Substitution with Exponential Functions

[Jason]

ex. a

What's the solution?

\(\underline{\int\,e^{2x \,dx}}\)


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

\(\int e^{u}\,dx\)

\(u = 2x \,dx\)

\(du = 2\,dx\)

\(\dfrac{du}{2} = \,dx\)

\(\int e^{u}\,\dfrac{du}{2}\)

\(\dfrac{1}{2}\int e^{u}\,du\)

\(\dfrac{e^{2x}}{2} + C\)