What is the integral of 4sqrt(x)+\sqrt[4]{x} ?

The integral of 4sqrt(x)+\sqrt[4]{x} is 8/3 x^{3/2}+4/5 x^{5/4}+C

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integral of 4sqrt(x)+\sqrt[4]{x}

\frac{8}{3} x^{\frac{3}{2}} + \frac{4}{5} x^{\frac{5}{4}} + 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 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= \frac{8}{3} x^{\frac{3}{2}} + \frac{4}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} + \frac{4}{5} x^{\frac{5}{4}} + C

\int_{0}^{\frac{1}{2}} 8 x - \frac{1}{2} x d x

x \to - 2 lim (x^{5} + 4 x^{3} - 5 x - 2)

(1 + cos (x))^{^{'}}

\int_{0}^{3} ∣ x - 1 ∣ d x

\int_{0}^{1} 1 + x^{2} d x

What is the integral of 4sqrt(x)+\sqrt[4]{x} ?
The integral of 4sqrt(x)+\sqrt[4]{x} is 8/3 x^{3/2}+4/5 x^{5/4}+C