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Popular >

integral of 3x^2-x+3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

derivative of 2/(\sqrt[5]{(4x-1^3)})

derivative of (8x^2+2x+2/(sqrt(x)))

\frac{d}{d x} (\frac{8 x ^{2} + 2 x + 2}{x})

slope of (80,2000),(260,5600)slope

(80, 2000), (260, 5600)

limit as x approaches 1 of e^x

x \to 1 lim (e^{x})

integral from 2 to 7 of 1/(25+(x-2)^2)

\int_{2}^{7} \frac{1}{25 + ( x - 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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