en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(4x+1)

Solution

\int x (4 x + 1) d x

Solution

\frac{4 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Solution steps

\int x (4 x + 1) d x

Expand

x (4 x + 1) : 4 x^{2} + x

= \int 4 x^{2} + 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 4 x^{2} d x + \int x d x

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

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

= \frac{4 x ^{3}}{3} + \frac{x ^{2}}{2}

Add a constant to the solution

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

Popular Examples

(df)/(dt)=4t+(9t)/(sqrt(9-t^2))

\frac{df}{d t} = 4 t + \frac{9 t}{9 - t ^{2}}

roots x*y^2 roots

x \cdot y^{2}

limit as x approaches 3 of-sqrt(x+3)

x \to 3 lim (- x + 3)

derivative of sqrt((x^2-1/(x^2-2x+1)))

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} - 2 x + 1})

integral of 2sqrt(s)

\int 2 s d s

Frequently Asked Questions (FAQ)

What is the integral of x(4x+1) ?
The integral of x(4x+1) is (4x^3)/3+(x^2)/2+C