What is the integral of x^{1/4}+4 ?

The integral of x^{1/4}+4 is 4/5 x^{5/4}+4x+C

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integral of x^{1/4}+4

\int x^{\frac{1}{4}} + 4 d x

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

Solution steps

\int x^{\frac{1}{4}} + 4 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 x^{\frac{1}{4}} d x + \int 4 d x

\int x^{\frac{1}{4}} d x = \frac{4}{5} x^{\frac{5}{4}}

\int 4 d x = 4 x

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

Add a constant to the solution

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

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What is the integral of x^{1/4}+4 ?
The integral of x^{1/4}+4 is 4/5 x^{5/4}+4x+C