en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2-3x+1

Solution

\int x^{2} - 3 x + 1 d x

Solution

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

Solution steps

\int x^{2} - 3 x + 1 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 3 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of 1/(9x^2+6x+2)

\int \frac{1}{9 x ^{2} + 6 x + 2} d x

integral of (tan(2x)-1)^2

\int (tan (2 x) - 1)^{2} d x

integral of x(x+4)

\int x (x + 4) d x

integral of sqrt(x+25)

\int x + 25 d x

integral of 2/(ln(x))

\int \frac{2}{ln ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of x^2-3x+1 ?
The integral of x^2-3x+1 is (x^3)/3-(3x^2)/2+x+C