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

The integral of (2x^3-(x^2)/2+5x) is (x^4)/2-(x^3)/6+(5x^2)/2+C

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integral of (2x^3-(x^2)/2+5x)

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

\frac{x ^{4}}{2} - \frac{x ^{3}}{6} + \frac{5 x ^{2}}{2} + C

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

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

= \frac{x ^{4}}{2} - \frac{x ^{3}}{6} + \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{2} - \frac{x ^{3}}{6} + \frac{5 x ^{2}}{2} + C

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What is the integral of (2x^3-(x^2)/2+5x) ?
The integral of (2x^3-(x^2)/2+5x) is (x^4)/2-(x^3)/6+(5x^2)/2+C