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+2x+5

Solution

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

Solution

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of 1/((a^2+z^2)^{3/2)}

\int \frac{1}{( a ^{2} + z ^{2} ) ^{\frac{3}{2}}} d z

integral of (5x)/((2x+1)(x-7))

\int \frac{5 x}{( 2 x + 1 ) ( x - 7 )} d x

integral of (3e^x)/(sqrt(4-e^{2x))}

\int \frac{3 e ^{x}}{4 - e ^{2 x}} d x

integral of (3sec^2(x))/(9tan(x)-1)

\int \frac{3 sec ^{2} ( x )}{9 tan ( x ) - 1} d x

integral of (8ln(x))/(x^3)

\int \frac{8 ln ( x )}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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