en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3-2x+5

Solution

integral

x^{3} - 2 x + 5

Solution

\frac{x ^{4}}{4} - x^{2} + 5 x + C

Solution steps

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

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

\int 2 x d x = x^{2}

\int 5 d x = 5 x

= \frac{x ^{4}}{4} - x^{2} + 5 x

Add a constant to the solution

= \frac{x ^{4}}{4} - x^{2} + 5 x + C

Popular Examples

integral of (sin(x))/4 integral

\frac{sin ( x )}{4}

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

\frac{x ^{2} a}{( 1 + a ^{2} x ^{2} )}

integral of ((x^3))/((x^2+2x+1))integral

\frac{( x ^{3} )}{( x ^{2} + 2 x + 1 )}

integral of 1+e^x integral

1 + e^{x}

integral of (cos^2(x))/((1+sin^2(x)))integral

\frac{cos ^{2} ( x )}{( 1 + sin ^{2} ( x ) )}

Frequently Asked Questions (FAQ)

What is the integral of x^3-2x+5 ?
The integral of x^3-2x+5 is (x^4)/4-x^2+5x+C