Question

Integrate $\int e^{2x}dx$.

Answer 1

Solve the given integral

Given: $\int e^{2x}dx$

Now,

Put, $u=2x$

Then, $2dx=du$

Now, replace these values in$\int e^{2x}dx$ and solve,

$$\begin{gathered} =\int e^u.\frac{1}{2}du \\ =\frac{1}{2}\int e^{u}du \\ =\frac{1}{2}{e}^u+C \\ =\frac{1}{2}{e}^{2x}+C \end{gathered}$$

Hence, Integral $\int e^{2x}dx$ is$\frac{1}{2}{e}^{2x}+C$.