What is the integral of ((x^2)/3+7x) ?

The integral of ((x^2)/3+7x) is (x^3)/9+(7x^2)/2+C

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integral of ((x^2)/3+7x)

\int (\frac{x ^{2}}{3} + 7 x) d x

\frac{x ^{3}}{9} + \frac{7 x ^{2}}{2} + C

Solution steps

\int \frac{x ^{2}}{3} + 7 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{x ^{2}}{3} d x + \int 7 x d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

= \frac{x ^{3}}{9} + \frac{7 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{3}}{9} + \frac{7 x ^{2}}{2} + C

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What is the integral of ((x^2)/3+7x) ?
The integral of ((x^2)/3+7x) is (x^3)/9+(7x^2)/2+C