What is the integral of \sqrt[4]{5}+\sqrt[4]{x} ?

The integral of \sqrt[4]{5}+\sqrt[4]{x} is \sqrt[4]{5}x+4/5 x^{5/4}+C

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integral of \sqrt[4]{5}+\sqrt[4]{x}

\int 45 + 4 x d x

45 x + \frac{4}{5} x^{\frac{5}{4}} + C

Solution steps

\int 45 + 4 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 45 d x + \int 4 x d x

\int 45 d x = 45 x

\int 4 x d x = \frac{4}{5} x^{\frac{5}{4}}

= 45 x + \frac{4}{5} x^{\frac{5}{4}}

Add a constant to the solution

= 45 x + \frac{4}{5} x^{\frac{5}{4}} + C

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