Integral of 15e^(5x)-3 dx

1. Integrate term-by-term:

   1. The integral of a constant times a function is the constant times the integral of the function:

      $$\int 15 e^{5 x}\, dx = 15 \int e^{5 x}\, dx$$

      1. Don't know the steps in finding this integral.

         But the integral is

         $$\frac{e^{5 x}}{5}$$

      So, the result is: $3 e^{5 x}$

   1. The integral of a constant is the constant times the variable of integration:

      $$\int \left(\left(-1\right) 3\right)\, dx = - 3 x$$

   The result is: $- 3 x + 3 e^{5 x}$

2. Add the constant of integration:

   $$- 3 x + 3 e^{5 x}+ \mathrm{constant}$$

The answer is:

$$- 3 x + 3 e^{5 x}+ \mathrm{constant}$$