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

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

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integral of (x^2+2)/3

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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