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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1/x-sin(x))

\int (\frac{1}{x} - sin (x)) d x

ln ∣ x ∣ + cos (x) + C

Solution steps

\int \frac{1}{x} - sin (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 \frac{1}{x} d x - \int sin (x) d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - (- cos (x))

Simplify

= ln ∣ x ∣ + cos (x)

Add a constant to the solution

= ln ∣ x ∣ + cos (x) + C

\int e^{5 - 3 x} d x

\int \frac{2 x}{( x ^{2} + 4 )} d x

\int (8 + \frac{2}{5} x^{2} + \frac{3}{7} x^{3}) d x

\int 6 y^{- 3} d y

\int - \frac{1}{e ^{t} + c} d t

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