en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3+2x+1

Solution

\int x^{3} + 2 x + 1 d x

Solution

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

Solution steps

\int x^{3} + 2 x + 1 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^{3} d x + \int 2 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

derivative of f(x)=(2x^2)/(x+3)derivative of

f (x) = \frac{2 x ^{2}}{x + 3}

derivative of (2x-1)^2 derivative of

(2 x - 1)^{2}

limit as x approaches 0-of 18-x^2

x \to 0 - lim (18 - x^{2})

derivative of 1/(x+c)

\frac{d}{d x} (\frac{1}{x + c})

integral of (2x+1)^9

\int (2 x + 1)^{9} d x

Frequently Asked Questions (FAQ)

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