en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1/2 x-1)

Solution

\int (\frac{1}{2} x - 1) d x

Solution

\frac{x ^{2}}{4} - x + C

Solution steps

\int \frac{1}{2} 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 \frac{1}{2} x d x - \int 1 d x

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

\int 1 d x = x

= \frac{x ^{2}}{4} - x

Add a constant to the solution

= \frac{x ^{2}}{4} - x + C

Popular Examples

integral of sin((pix)/6)

\int sin (\frac{π x}{6}) d x

integral of \sqrt[3]{x}+1

integral of 1/(7-9x)

\int \frac{1}{7 - 9 x} d x

integral of x/(x^2+x+4)

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

integral of (7/x-5/(x^6))

\int (\frac{7}{x} - \frac{5}{x ^{6}}) d x

Frequently Asked Questions (FAQ)

What is the integral of (1/2 x-1) ?
The integral of (1/2 x-1) is (x^2)/4-x+C