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+5

Solution

\int x^{3} + 5 d x

Solution

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

Solution steps

\int x^{3} + 5 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 5 d x

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of sin(4pix)sin(npix)

\int sin (4 π x) sin (nπ x) d x

derivative of log_{3}(8x-1)

\frac{d}{d x} (lo g_{3} (8 x - 1))

integral from 0 to 1 of 5^{-θ}

\int_{0}^{1} 5^{- θ} d θ

(dy)/(dx)=-2xy^2

\frac{d y}{d x} = - 2 x y^{2}

(dy}{dx}=\frac{x^8-4y)/x

\frac{d y}{d x} = \frac{x ^{8} - 4 y}{x}

Frequently Asked Questions (FAQ)

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