What is the integral of (cos(x)+4^x) ?

The integral of (cos(x)+4^x) is sin(x)+(2^{2x-1})/(ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (cos(x)+4^x)

\int (cos (x) + 4^{x}) d x

sin (x) + \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

Solution steps

\int cos (x) + 4^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x + \int 4^{x} d x

\int cos (x) d x = sin (x)

\int 4^{x} d x = \frac{2 ^{2 x - 1}}{ln ( 2 )}

= sin (x) + \frac{2 ^{2 x - 1}}{ln ( 2 )}

Add a constant to the solution

= sin (x) + \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

What is the integral of (cos(x)+4^x) ?
The integral of (cos(x)+4^x) is sin(x)+(2^{2x-1})/(ln(2))+C