en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (50+x)^2

Solution

\int (50 + x)^{2} d x

Solution

2500 x + 50 x^{2} + \frac{x ^{3}}{3} + C

Solution steps

\int (50 + x)^{2} d x

Expand

(50 + x)^{2} : 2500 + 100 x + x^{2}

= \int 2500 + 100 x + x^{2} 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 2500 d x + \int 100 x d x + \int x^{2} d x

\int 2500 d x = 2500 x

\int 100 x d x = 50 x^{2}

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

= 2500 x + 50 x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= 2500 x + 50 x^{2} + \frac{x ^{3}}{3} + C

Graph

Popular Examples

integral of x^5-x^3

integral of (144)/(36+x^2)

integral of-15cos^3(x)sin(x)

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

integral of (sqrt(x))/(x+3)

Frequently Asked Questions (FAQ)

What is the integral of (50+x)^2 ?
The integral of (50+x)^2 is 2500x+50x^2+(x^3)/3+C