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^3)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of 2xarcsin(x^2)

\int 2 x arcsin (x^{2}) d x

integral of (sqrt(arctan(x)))/(x^2+1)

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

integral of ((x+1))/((x^2-2x+5))

\int \frac{( x + 1 )}{( x ^{2} - 2 x + 5 )} d x

integral of csc^6(x/2)

\int csc^{6} (\frac{x}{2}) d x

integral of (1/2 e^x+3/4 2^x)

\int (\frac{1}{2} e^{x} + \frac{3}{4} 2^{x}) d x

Frequently Asked Questions (FAQ)

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