en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(2x+5)

Solution

\int x (2 x + 5) d x

Solution

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

Solution steps

\int x (2 x + 5) d x

Expand

x (2 x + 5) : 2 x^{2} + 5 x

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

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

\int 5 x d x = \frac{5 x ^{2}}{2}

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(8e^{xy})

\frac{\partial}{\partial x} (8 e^{x y})

\frac{d y}{d t} = - y^{2}

derivative of 5xln(3x)-5x derivative of

5 x ln (3 x) - 5 x

\frac{df}{d x} x = x^{3}

integral of 1/(\sqrt[7]{x^2)}

Frequently Asked Questions (FAQ)

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