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Popular Calculus >

integral of x^2-5x+3

Solution

\int x^{2} - 5 x + 3 d x

Solution

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 3 x + C

Solution steps

\int x^{2} - 5 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 5 x d x + \int 3 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 3 d x = 3 x

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 3 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 3 x + C

Graph

Popular Examples

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\int (8 x^{2} - 4 x) e^{2 x - 1} d x

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integral of (x-5)/(x^2+5x+4)

\int \frac{x - 5}{x ^{2} + 5 x + 4} d x

integral of t^2-2t-15

\int t^{2} - 2 t - 15 d t

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\int θ cos (π θ) d θ

Frequently Asked Questions (FAQ)

What is the integral of x^2-5x+3 ?
The integral of x^2-5x+3 is (x^3)/3-(5x^2)/2+3x+C