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

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

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integral of 1-x^{1/4}

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

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

Solution steps

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

\int 1 d x = x

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

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

Add a constant to the solution

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

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