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+3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

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

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

integral of 1 (x^6-3ln(x)+1/x)

\int \frac{d}{1} (x^{6} - 3 ln (x) + \frac{1}{x}) d x

integral of x/((4+5x)^2)

\int \frac{x}{( 4 + 5 x ) ^{2}} d x

integral of (x^2+x+2)

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

integral of sec(32w)tan(32w)

\int sec (32 w) tan (32 w) d w

Frequently Asked Questions (FAQ)

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