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

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

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

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

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

Solution steps

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

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

\int 1 d x = x

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

Add a constant to the solution

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

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2 cos^{2} (x)

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