What is the integral of 3x^2-9x+5 ?

The integral of 3x^2-9x+5 is x^3-(9x^2)/2+5x+C

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integral of 3x^2-9x+5

integral

3 x^{2} - 9 x + 5

x^{3} - \frac{9 x ^{2}}{2} + 5 x + C

Solution steps

\int 3 x^{2} - 9 x + 5 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 9 x d x + \int 5 d x

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

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 5 d x = 5 x

= x^{3} - \frac{9 x ^{2}}{2} + 5 x

Add a constant to the solution

= x^{3} - \frac{9 x ^{2}}{2} + 5 x + C

\frac{e ^{x}}{3}

\frac{1}{5 x}

e^{x} + \frac{1}{2} + 2 x^{2} + 3

\frac{1}{x ^{2} + 9}

(3 x - 1)^{- 2}

What is the integral of 3x^2-9x+5 ?
The integral of 3x^2-9x+5 is x^3-(9x^2)/2+5x+C