# Problem of the Week

## Updated at Aug 26, 2013 11:12 AM

How can we find the integral of $${e}^{x}+\cos{x}$$?

Below is the solution.

$\int {e}^{x}+\cos{x} \, dx$

 1 Use Sum Rule: $$\int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx$$.$\int {e}^{x} \, dx+\int \cos{x} \, dx$2 The integral of $${e}^{x}$$ is $${e}^{x}$$.${e}^{x}+\int \cos{x} \, dx$3 Use Trigonometric Integration: the integral of $$\cos{x}$$ is $$\sin{x}$$.${e}^{x}+\sin{x}$4 Add constant.${e}^{x}+\sin{x}+C$Donee^x+sin(x)+C