en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 2x+3-x^2

Solution

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

Solution

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

Solution steps

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

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

\int 3 d x = 3 x

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (2x-4)^3

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

integral of (3x)/(sqrt(x^2+4))

\int \frac{3 x}{x ^{2} + 4} d x

integral of sqrt(2^2+x^2)

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

integral of (e^{7x})/(e^{7x)+4}

\int \frac{e ^{7 x}}{e ^{7 x} + 4} d x

integral of ((x+1))/(sqrt(4-x^2))

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

Frequently Asked Questions (FAQ)

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