en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of |x|-1

Solution

\int ∣ x ∣ - 1 d x

Solution

\frac{x ∣ x ∣}{2} - x + C

Solution steps

\int ∣ x ∣ - 1 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 ∣ x ∣ d x - \int 1 d x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

\int 1 d x = x

= \frac{x ∣ x ∣}{2} - x

Add a constant to the solution

= \frac{x ∣ x ∣}{2} - x + C

Popular Examples

integral of sqrt((1-x)/(1+x))*1/x

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

integral of 9x^2e^{x^3}

\int 9 x^{2} e^{x^{3}} d x

integral of 1/(2x^2+2x+3)

\int \frac{1}{2 x ^{2} + 2 x + 3} d x

integral of x/(sqrt(3x-x^2))

\int \frac{x}{3 x - x ^{2}} d x

integral of sin^4(6x)cos^2(6x)

\int sin^{4} (6 x) cos^{2} (6 x) d x

Frequently Asked Questions (FAQ)

What is the integral of |x|-1 ?
The integral of |x|-1 is (x|x|)/2-x+C