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

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

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

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

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

Solution steps

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

\int \frac{1}{3} x^{2} d x = \frac{x ^{3}}{9}

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

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

Add a constant to the solution

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

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