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

The integral of (x^3+x^2+2x-3) is (x^4)/4+(x^3)/3+x^2-3x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^3+x^2+2x-3)

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

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

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

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