Question

(8) $\int e^{2x + 1}dx$

Explanation:

Step1: Let \( u = 2x + 1 \)

Then \( du=2dx \), and \( dx=\frac{1}{2}du \)

Step2: Substitute into the integral

$$
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Step3: Integrate \( e^{u} \)

Since \( \int e^{u}du=e^{u}+C \), we have \( \frac{1}{2}\int e^{u}du=\frac{1}{2}e^{u}+C \)

Step4: Substitute back \( u = 2x + 1 \)

\( \frac{1}{2}e^{u}+C=\frac{1}{2}e^{2x + 1}+C \)

Answer:

\(\frac{1}{2}e^{2x + 1}+C\)