en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2-5x+4

Solution

\int x^{2} - 5 x + 4 d x

Solution

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 4 x + C

Solution steps

\int x^{2} - 5 x + 4 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 5 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 4 x + C

Graph

Popular Examples

sum from n=0 to infinity of 1/(100^n)

n = 0 \sum \infty \frac{1}{10 0 ^{n}}

limit as x approaches 2 of x^2+7x-5

x \to 2 lim (x^{2} + 7 x - 5)

integral of (1+ln^3(x))/x

\int \frac{1 + ln ^{3} ( x )}{x} d x

(dv)/(dt)=-2sqrt(v)

\frac{d v}{d t} = - 2 v

integral from 2 to 4 of 1/((x-3)^2)

\int_{2}^{4} \frac{1}{( x - 3 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of x^2-5x+4 ?
The integral of x^2-5x+4 is (x^3)/3-(5x^2)/2+4x+C