What is the integral of (3cos(x)-1/x) ?

The integral of (3cos(x)-1/x) is 3sin(x)-ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3cos(x)-1/x)

\int (3 cos (x) - \frac{1}{x}) d x

3 sin (x) - ln ∣ x ∣ + C

Solution steps

\int 3 cos (x) - \frac{1}{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 3 cos (x) d x - \int \frac{1}{x} d x

\int 3 cos (x) d x = 3 sin (x)

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 sin (x) - ln ∣ x ∣

Add a constant to the solution

= 3 sin (x) - ln ∣ x ∣ + C

What is the integral of (3cos(x)-1/x) ?
The integral of (3cos(x)-1/x) is 3sin(x)-ln|x|+C