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

Popular Examples

derivative of x^2-6(3)+9 derivative of

x^{2} - 6 (3) + 9

derivative of sqrt(3x^2+2)derivative of

3 x^{2} + 2

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

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

integral of e^{t/5}

\int e^{\frac{t}{5}} d t

integral of ((x+3))/(x^2+8x-9)

\int \frac{( x + 3 )}{x ^{2} + 8 x - 9} d 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