en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of x^3(x+4)

Solution

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

Solution

\frac{x ^{5}}{5} + x^{4} + C

Solution steps

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

Expand

x^{3} (x + 4) : x^{4} + 4 x^{3}

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

= \frac{x ^{5}}{5} + x^{4}

Add a constant to the solution

= \frac{x ^{5}}{5} + x^{4} + C

Graph

Popular Examples

integral of (3^x)/(9^x+3)

integral of 3e^{4x}-5cos(6x)+7

integral of im(z-i)

integral of (sin(x)cos(x))/(cos^2(x)+4)

integral of (x-10)

Frequently Asked Questions (FAQ)

What is the integral of x^3(x+4) ?
The integral of x^3(x+4) is (x^5)/5+x^4+C