Set up the integral for the given expression.

We need to integrate $\sin(3x) - e^{3x}$ with respect to $x$.

$$\int (\sin(3x) - e^{3x})\,dx$$

The integral of a difference is the difference of the integrals.

$$\int \sin(3x)\,dx - \int e^{3x}\,dx$$

For the first term, $\int \sin(ax)\,dx = -\frac{1}{a}\cos(ax) + C$. Here $a=3$.

$$\int \sin(3x)\,dx = -\frac{1}{3}\cos(3x)$$

For the second term, $\int e^{ax}\,dx = \frac{1}{a}e^{ax} + C$. Here $a=3$.

$$\int e^{3x}\,dx = \frac{1}{3}e^{3x}$$