(g) evaluate the integral\n int e^{sin(x)}cos(x)mathrm{d}x

Explanation:

Step1: Use substitution method

Let $u = \sin(x)$, then $du=\cos(x)dx$.

Step2: Rewrite the integral

The integral $\int e^{\sin(x)}\cos(x)dx$ becomes $\int e^{u}du$.

Step3: Integrate $e^{u}$

We know that $\int e^{u}du=e^{u}+C$.

Step4: Substitute back $u = \sin(x)$

We get $e^{\sin(x)}+C$.

Answer:

$e^{\sin(x)}+C$