What is the integral of 2x^2-4x+5 ?

The integral of 2x^2-4x+5 is (2x^3)/3-2x^2+5x+C

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integral of 2x^2-4x+5

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

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

Solution steps

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

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

\int 4 x d x = 2 x^{2}

\int 5 d x = 5 x

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

Add a constant to the solution

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

\int (\frac{2 ln ( x )}{x}) d x

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

\int \frac{5}{x ln ^{3} ( x )} d x

\int p (p + 4)^{8} d p

What is the integral of 2x^2-4x+5 ?
The integral of 2x^2-4x+5 is (2x^3)/3-2x^2+5x+C