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+3

Solution

\int x^{2} + x + 3 d x

Solution

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

Solution steps

\int x^{2} + x + 3 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 3 d x

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Graph

Popular Examples

limit as x approaches 0+of (x^2)/6-7/x

derivative of (3(9^x)/(x^5))

integral of 1/(x^5)sin(1/(x^4))

2x^3y^'=y(2x^2-y^2)

Frequently Asked Questions (FAQ)

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