1. ∫(3^x - sin x) dx

Explanation:

Step1: Split the integral

$\int(3^{x}-\sin x)dx=\int3^{x}dx-\int\sin xdx$

Step2: Integrate $\int3^{x}dx$

Using the formula $\int a^{x}dx=\frac{a^{x}}{\ln a}+C$ ($a > 0,a\neq1$), for $a = 3$, we have $\int3^{x}dx=\frac{3^{x}}{\ln 3}+C_1$

Step3: Integrate $\int\sin xdx$

We know that $\int\sin xdx=-\cos x + C_2$

Step4: Combine the results

$\int(3^{x}-\sin x)dx=\frac{3^{x}}{\ln 3}+\cos x + C$ ($C = C_1 + C_2$)

Answer:

$\frac{3^{x}}{\ln 3}+\cos x + C$