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Popular >

integral of x^2-x+1

Solution

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

Solution

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

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\int 8 e^{5 x} d x

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

Frequently Asked Questions (FAQ)

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