en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 5x^2+x

Solution

\int 5 x^{2} + x d x

Solution

\frac{5 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Solution steps

\int 5 x^{2} + 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 5 x^{2} d x + \int x d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

= \frac{5 x ^{3}}{3} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{5 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Graph

Popular Examples

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

integral of (x^5-x)/(x^2+1)

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

integral of x/((x^2+5))

integral of 1/(x^2*sqrt(x^2-16))

Frequently Asked Questions (FAQ)

What is the integral of 5x^2+x ?
The integral of 5x^2+x is (5x^3)/3+(x^2)/2+C