en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5x-x^2

Solution

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

Solution

\frac{5 x ^{2}}{2} - \frac{x ^{3}}{3} + C

Solution steps

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

\int 5 x d x = \frac{5 x ^{2}}{2}

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

= \frac{5 x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{5 x ^{2}}{2} - \frac{x ^{3}}{3} + C

Graph

Popular Examples

integral of ((x+2))/((x^2+2x+10)^{5/2)}

\int \frac{( x + 2 )}{( x ^{2} + 2 x + 10 ) ^{\frac{5}{2}}} d x

integral from-2 to 0 of (x^3-4x)

\int_{- 2}^{0} (x^{3} - 4 x) d x

inverse oflaplace (e^{-2s})/s inverse laplace

\frac{e ^{- 2 s}}{s}

y^'=2x(1+x^2-y),y(1)=2

y^{^{'}} = 2 x (1 + x^{2} - y), y (1) = 2

integral of cos^2(x)ln(x)

\int cos^{2} (x) ln (x) d x

Frequently Asked Questions (FAQ)

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