What is the integral of (sqrt(x)+1/(\sqrt[6]{x)}) ?

The integral of (sqrt(x)+1/(\sqrt[6]{x)}) is 2/3 x^{3/2}+6/5 x^{5/6}+C

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integral of (sqrt(x)+1/(\sqrt[6]{x)})

\frac{2}{3} x^{\frac{3}{2}} + \frac{6}{5} x^{\frac{5}{6}} + C

Solution steps

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

= \frac{2}{3} x^{\frac{3}{2}} + \frac{6}{5} x^{\frac{5}{6}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{6}{5} x^{\frac{5}{6}} + C

\frac{d}{d x} (\frac{5}{3} x^{\frac{2}{3}})

x \to + 0 lim (- ∣ x - 2 ∣ + 3)

\frac{d}{d x} (4 x^{4} - 7 x^{3} + 3)

\int - 3 sin (t) d t

(t - 1) 1 (t - 1)

What is the integral of (sqrt(x)+1/(\sqrt[6]{x)}) ?
The integral of (sqrt(x)+1/(\sqrt[6]{x)}) is 2/3 x^{3/2}+6/5 x^{5/6}+C