en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (a+18)^2

Solution

\int (a + 18)^{2} d a

Solution

\frac{a ^{3}}{3} + 18 a^{2} + 324 a + C

Solution steps

\int (a + 18)^{2} d a

Expand

(a + 18)^{2} : a^{2} + 36 a + 324

= \int a^{2} + 36 a + 324 d a

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int a^{2} d a + \int 36 a d a + \int 324 d a

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

\int 36 a d a = 18 a^{2}

\int 324 d a = 324 a

= \frac{a ^{3}}{3} + 18 a^{2} + 324 a

Add a constant to the solution

= \frac{a ^{3}}{3} + 18 a^{2} + 324 a + C

Graph

Popular Examples

integral of sin(x+nx)

\int sin (x + n x) d x

integral of x*1/(sqrt(1-x^2))

\int x \cdot \frac{1}{1 - x ^{2}} d x

(\partial)/(\partial x)(tan(3x))

\frac{\partial}{\partial x} (tan (3 x))

sum from n=1 to infinity of n/(2n^3)

n = 1 \sum \infty \frac{n}{2 n ^{3}}

integral of (ln(x^3))/(2x)

\int \frac{ln ( x ^{3} )}{2 x} d x

Frequently Asked Questions (FAQ)

What is the integral of (a+18)^2 ?
The integral of (a+18)^2 is (a^3)/3+18a^2+324a+C