How do you evaluate the integral int3e^(x)-5e^(2x) dx?

Sep 25, 2014

$\int 3 {e}^{x} - 5 {e}^{2 x} \mathrm{dx} = 3 {e}^{x} - \frac{5}{2} {e}^{2 x} + C$

Let us look at some details.

Remember:

$\int {e}^{x} \mathrm{dx} = {e}^{x} + C$

$\int {e}^{k x} \mathrm{dx} = {e}^{k x} / k + C$

Now, let us work on the integral.

$\int 3 {e}^{x} - 5 {e}^{2 x} \mathrm{dx}$

by applying integral on each term,

$= \int 3 {e}^{x} \mathrm{dx} - \int 5 {e}^{2 x} \mathrm{dx}$

by pulling constants out of the integrals

$= 3 \int {e}^{x} \mathrm{dx} - 5 \int {e}^{2 x} \mathrm{dx}$

by applying the formulas above,

$= 3 {e}^{x} - 5 {e}^{2 x} / 2 + C$