What is the integral of \sqrt[3]{x}+1/(sqrt(x)) ?

The integral of \sqrt[3]{x}+1/(sqrt(x)) is 3/4 x^{4/3}+2sqrt(x)+C

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integral of \sqrt[3]{x}+1/(sqrt(x))

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

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

Solution steps

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

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

\int \frac{1}{x} d x = 2 x

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

Add a constant to the solution

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

\frac{s ^{2} - 1}{s ( s + 2 ) ( s - 3 )}

\frac{d}{d x} (- e^{x y})

y = x^{3} - x, y = 0

x = - 2, x = 2, y = 8 x, y = x^{2} - 9

\frac{d}{d x} (lo g_{2} (x - 1))

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