en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/2 x^3

Solution

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

Solution

\frac{x ^{4}}{8} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= \frac{1}{2} \cdot \frac{x ^{4}}{4}

Simplify

\frac{1}{2} \cdot \frac{x ^{4}}{4} : \frac{x ^{4}}{8}

= \frac{x ^{4}}{8}

Add a constant to the solution

= \frac{x ^{4}}{8} + C

Graph

Popular Examples

integral from 0 to 4 of sqrt(1+\sqrt{x)}

\int_{0}^{4} 1 + x d x

(\partial)/(\partial x)(2^x+2^y)

\frac{\partial}{\partial x} (2^{x} + 2^{y})

(\partial)/(\partial x)(3x^2-6x+3y^2)

\frac{\partial}{\partial x} (3 x^{2} - 6 x + 3 y^{2})

integral of x^2e

\int x^{2} e d x

laplacetransform sin(100*t)laplace transform

sin (100 \cdot t)

Frequently Asked Questions (FAQ)

What is the integral of 1/2 x^3 ?
The integral of 1/2 x^3 is (x^4)/8+C