What is the integral of 1/2 x+2/3 x^2 ?

The integral of 1/2 x+2/3 x^2 is (x^2)/4+(2x^3)/9+C

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integral of 1/2 x+2/3 x^2

\int \frac{1}{2} x + \frac{2}{3} x^{2} d x

\frac{x ^{2}}{4} + \frac{2 x ^{3}}{9} + C

Solution steps

\int \frac{1}{2} x + \frac{2}{3} x^{2} 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 \frac{1}{2} x d x + \int \frac{2}{3} x^{2} d x

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

\int \frac{2}{3} x^{2} d x = \frac{2 x ^{3}}{9}

= \frac{x ^{2}}{4} + \frac{2 x ^{3}}{9}

Add a constant to the solution

= \frac{x ^{2}}{4} + \frac{2 x ^{3}}{9} + C

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What is the integral of 1/2 x+2/3 x^2 ?
The integral of 1/2 x+2/3 x^2 is (x^2)/4+(2x^3)/9+C