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

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

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

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

\frac{2 x ^{3}}{3} + \frac{1}{3} x + C

Solution steps

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

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

\int \frac{1}{3} d x = \frac{1}{3} x

= \frac{2 x ^{3}}{3} + \frac{1}{3} x

Add a constant to the solution

= \frac{2 x ^{3}}{3} + \frac{1}{3} x + C

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