en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x-5)^2

Solution

\int (2 x - 5)^{2} d x

Solution

\frac{4 x ^{3}}{3} - 10 x^{2} + 25 x + C

Solution steps

\int (2 x - 5)^{2} d x

Expand

(2 x - 5)^{2} : 4 x^{2} - 20 x + 25

= \int 4 x^{2} - 20 x + 25 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 4 x^{2} d x - \int 20 x d x + \int 25 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 20 x d x = 10 x^{2}

\int 25 d x = 25 x

= \frac{4 x ^{3}}{3} - 10 x^{2} + 25 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} - 10 x^{2} + 25 x + C

Popular Examples

(\partial)/(\partial x)(4x^2y-4x+3y^3)

\frac{\partial}{\partial x} (4 x^{2} y - 4 x + 3 y^{3})

integral from 1 to e^4 of x^2ln(x)

\int_{1}^{e^{4}} x^{2} ln (x) d x

ye^{2x}dx=(4+e^{2x})dy

y e^{2 x} d x = (4 + e^{2 x}) d y

xy^2y^'=y^3-x^3,y(1)=2

x y^{2} y^{^{'}} = y^{3} - x^{3}, y (1) = 2

sum from n=1 to infinity of n(4/5)^n

n = 1 \sum \infty n (\frac{4}{5})^{n}

Frequently Asked Questions (FAQ)

What is the integral of (2x-5)^2 ?
The integral of (2x-5)^2 is (4x^3)/3-10x^2+25x+C