en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1/x+C

Solution

\int - \frac{1}{x} + C d x

Solution

- ln ∣ x ∣ + C x + C

Solution steps

\int - \frac{1}{x} + C 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 C d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int C d x = C x

= - ln ∣ x ∣ + C x

Add a constant to the solution

= - ln ∣ x ∣ + C x + C

Popular Examples

2xy(dy)/(dx)=y^2-x^2

2 x y \frac{d y}{d x} = y^{2} - x^{2}

integral of (3x^2+2e^x)

\int (3 x^{2} + 2 e^{x}) d x

limit as x approaches 0+of (|xsin(x)|)/x

x \to 0 + lim (\frac{∣ x sin ( x ) ∣}{x})

derivative of sin(e^{5x})

\frac{d}{d x} (sin (e^{5 x}))

integral from 1 to e of ln(15x)

\int_{1}^{e} ln (15 x) d x

Frequently Asked Questions (FAQ)

What is the integral of-1/x+C ?
The integral of-1/x+C is -ln|x|+Cx+C