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

The integral of x^{1/3}+3 is 3/4 x^{4/3}+3x+C

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integral of x^{1/3}+3

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

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

Solution steps

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x sin (y) + z e^{x})

\int (6 x - 7) d x

f (x) = \frac{1 - 2 ln ( x )}{x ^{3}}

sin (3 x^{2})

e^{x}, e^{- 2 x}, x = ln (3)

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