en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^3+4)

Solution

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

Solution

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

Solution steps

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

Popular Examples

integral of (x^m-x^n)/(sqrt(x))

\int \frac{x ^{m} - x ^{n}}{x} d x

integral of xln(8)integral

x ln (8)

integral of (4x^2+x+5)/((x+1)(x^2+1))

\int \frac{4 x ^{2} + x + 5}{( x + 1 ) ( x ^{2} + 1 )} d x

integral of (8x^5-3x^2-2x+5)

\int (8 x^{5} - 3 x^{2} - 2 x + 5) d x

integral of 2/(x^3-x^2)

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

Frequently Asked Questions (FAQ)

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