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

The integral of (x-1)/3 is 1/3 ((x^2)/2-x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x-1)/3

\int \frac{x - 1}{3} d x

\frac{1}{3} (\frac{x ^{2}}{2} - x) + C

Solution steps

\int \frac{x - 1}{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \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

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

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

\int 1 d x = x

= \frac{1}{3} (\frac{x ^{2}}{2} - x)

Add a constant to the solution

= \frac{1}{3} (\frac{x ^{2}}{2} - x) + C

\int \frac{tan ( x ) + sin ( x )}{cos ( x )} d x

\int \frac{x}{( x + 10 ) ( x ^{2} + 12 )} d x

\int 200 - 6 x d x

\int (x^{4} - 2 x^{3} + 3 x^{2} - 1) d x

\int \frac{1}{y ^{3} - 1} d y