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^2-x+6

Solution

\int x^{2} - x + 6 d x

Solution

\frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 6 x + C

Solution steps

\int x^{2} - x + 6 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^{2} d x - \int x d x + \int 6 d x

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

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

\int 6 d x = 6 x

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 6 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 6 x + C

Graph

Popular Examples

integral of (sin^2(x))/(cos^5(x))

integral of (x^7)/(1+x^4)

integral of (sqrt(1-(ln(x))^2))/(xln(x))

integral of (sec(θ)-tan(θ))^2

integral of 2ue^u

Frequently Asked Questions (FAQ)

What is the integral of x^2-x+6 ?
The integral of x^2-x+6 is (x^3)/3-(x^2)/2+6x+C