overall accuracy: 84.6% record: 18 score: 18 ∫e^(x/4)dx = e^(x/4)+c 4e^(x/4)+c -1/4e^(x/4)+c 1/4e^(x/4)+c…

Explanation:

Step1: Use substitution method

Let $u = \frac{x}{4}$, then $x = 4u$ and $dx=4du$.

Step2: Rewrite the integral

$\int e^{\frac{x}{4}}dx=\int e^{u}\cdot4du = 4\int e^{u}du$.

Step3: Integrate $e^{u}$

Since $\int e^{u}du=e^{u}+C$, then $4\int e^{u}du = 4e^{u}+C$.

Step4: Substitute back $u=\frac{x}{4}$

We get $4e^{\frac{x}{4}}+C$.

Answer:

$4e^{\frac{x}{4}}+C$