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+1)

Solution

\int (- x^{2} + 1) d x

Solution

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

Solution steps

\int - x^{2} + 1 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 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

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

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

integral of e^{3x-3}

\int e^{3 x - 3} d x

integral of 2xy+1

\int 2 x y + 1 d x

integral of 1/(z^2(z^2+1))

\int \frac{1}{z ^{2} ( z ^{2} + 1 )} d z

integral of 1/(7x-5)

\int \frac{1}{7 x - 5} d x

Frequently Asked Questions (FAQ)

What is the integral of (-x^2+1) ?
The integral of (-x^2+1) is -(x^3)/3+x+C