# How do you find the indefinite integral of int (7cosx+4e^x)dx?

Aug 31, 2017

$7 \sin x + 4 {e}^{x} + c$

#### Explanation:

$\text{using standard integrals}$

•color(white)(x)intcosxdx=sinx" and "inte^xdx=e^x

$\int \left(7 \cos x + 4 {e}^{x}\right) \mathrm{dx}$

$= 7 \sin x + 4 {e}^{x} + c$

$\text{where c is the constant of integration}$

Aug 31, 2017

$7 \sin \left(x\right) + 4 {e}^{x} + C$

#### Explanation:

Since they're a sum, you can break it apart and integrate each part separately...

$\int \left(7 \cos \left(x\right) + 4 {e}^{x}\right) \mathrm{dx} = \int 7 \cos \left(x\right) \mathrm{dx} + \int 4 {e}^{x} \mathrm{dx}$

$= 7 \int \cos \left(x\right) \mathrm{dx} + 4 \int {e}^{x} \mathrm{dx}$

$= 7 \sin \left(x\right) + 4 {e}^{x} + c$