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

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

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

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

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

Solution steps

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

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

\int 3 x^{\frac{1}{3}} d x = \frac{9}{4} x^{\frac{4}{3}}

\int 2 d x = 2 x

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

Add a constant to the solution

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

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