What is the integral of 5x^2-8x+4 ?

The integral of 5x^2-8x+4 is (5x^3)/3-4x^2+4x+C

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integral of 5x^2-8x+4

\int 5 x^{2} - 8 x + 4 d x

\frac{5 x ^{3}}{3} - 4 x^{2} + 4 x + C

Solution steps

\int 5 x^{2} - 8 x + 4 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 5 x^{2} d x - \int 8 x d x + \int 4 d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 8 x d x = 4 x^{2}

\int 4 d x = 4 x

= \frac{5 x ^{3}}{3} - 4 x^{2} + 4 x

Add a constant to the solution

= \frac{5 x ^{3}}{3} - 4 x^{2} + 4 x + C

\int \frac{2}{2 x + 1} d x

\int \frac{3}{5 y ^{2} + 4} d y

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

\int (6 x^{5}) d x

What is the integral of 5x^2-8x+4 ?
The integral of 5x^2-8x+4 is (5x^3)/3-4x^2+4x+C