en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x^3+2x)

Solution

\int (4 x^{3} + 2 x) d x

Solution

x^{4} + x^{2} + C

Solution steps

\int 4 x^{3} + 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^{3} d x + \int 2 x d x

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

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

= x^{4} + x^{2}

Add a constant to the solution

= x^{4} + x^{2} + C

Popular Examples

integral of 3(cos(x)+sin(2x))/(sin(x))

\int 3 \frac{cos ( x ) + sin ( 2 x )}{sin ( x )} d x

limit as x approaches 0 of (1+x)^x

x \to 0 lim ((1 + x)^{x})

(\partial)/(\partial x)(xye^{3y})

\frac{\partial}{\partial x} (x y e^{3 y})

derivative of 10x^{1/5}

\frac{d}{d x} (10 x^{\frac{1}{5}})

derivative of (x^2/(x+2))

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

Frequently Asked Questions (FAQ)

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