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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

derivative of e^{0.1x^2}

\frac{d}{d x} (e^{0.1 x^{2}})

area y=e^x,y=e^{7x},x=0,x=ln(2)area

y = e^{x}, y = e^{7 x}, x = 0, x = ln (2)

derivative of y=5x^7ln(x)derivative of

y = 5 x^{7} ln (x)

derivative of e^x-x^2+3x-2

\frac{d}{d x} (e^{x} - x^{2} + 3 x - 2)

integral from-2 to 3 of (17)/(x^4)

\int_{- 2}^{3} \frac{17}{x ^{4}} 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