en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-x^2+5

Solution

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

Solution

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

Solution steps

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

Graph

Popular Examples

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

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

integral of (sinh(x)+x^3)

\int (sinh (x) + x^{3}) d x

integral of (4-2x)/(4x-x^2)

\int \frac{4 - 2 x}{4 x - x ^{2}} d x

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

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

integral of usqrt(1+u^2)

\int u 1 + u^{2} d u

Frequently Asked Questions (FAQ)

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