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Popular >

integral of x^2-x+3

Solution

\int x^{2} - x + 3 d x

Solution

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

Solution steps

\int x^{2} - x + 3 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 3 d x

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

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\int 2 + sin (t) d t

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\int \frac{1}{- 4 + x ^{2}} d x

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\int x (2 sin (x) + 4 sin^{2} (x)) d x

integral of e^{8x-8}

\int e^{8 x - 8} d x

Frequently Asked Questions (FAQ)

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