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Popular Calculus >

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

Graph

Popular Examples

integral of e^{3x-3}

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

integral of x(5-x)

\int x (5 - x) d x

integral of x/(sqrt(4x-3-x^2))

\int \frac{x}{4 x - 3 - x ^{2}} d x

integral of (4x^3-8x)/(x^2(x^2+4))

\int \frac{4 x ^{3} - 8 x}{x ^{2} ( x ^{2} + 4 )} d x

integral of (5x-1)^5

\int (5 x - 1)^{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