What is the integral of cos(x)+1/5 x ?

The integral of cos(x)+1/5 x is sin(x)+(x^2)/(10)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos(x)+1/5 x

\int cos (x) + \frac{1}{5} x d x

sin (x) + \frac{x ^{2}}{10} + C

Solution steps

\int cos (x) + \frac{1}{5} 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 \frac{1}{5} x d x

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

\int \frac{1}{5} x d x = \frac{x ^{2}}{10}

= sin (x) + \frac{x ^{2}}{10}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{10} + C

What is the integral of cos(x)+1/5 x ?
The integral of cos(x)+1/5 x is sin(x)+(x^2)/(10)+C