en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (x^5-5x)

Solution

\int (x^{5} - 5 x) d x

Solution

\frac{x ^{6}}{6} - \frac{5 x ^{2}}{2} + C

Solution steps

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

\int x^{5} d x = \frac{x ^{6}}{6}

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{x ^{6}}{6} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{5 x ^{2}}{2} + C

Graph

Popular Examples

integral of x/e

\int \frac{x}{e} d x

integral of 3t^2ln(t)

\int 3 t^{2} ln (t) d t

integral of (x^2-2x+1)

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

integral of (2sin(x))/(cos^2(x))

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

integral of (30)/(x(ln(5x))^2)

\int \frac{30}{x ( ln ( 5 x ) ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (x^5-5x) ?
The integral of (x^5-5x) is (x^6)/6-(5x^2)/2+C