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

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

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

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

Add a constant to the solution

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

x \to 2 lim (x^{2} - 7 x + 2)

f (x) = 3 x^{3} + 8 x^{2}, at x = - 2

x \to 5 lim (\frac{7}{x - 5})

x \to \infty lim (7 + \frac{4}{x})

n = 1 \sum \infty \frac{3 n}{2 n + 1}

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