What is the integral of \sqrt[4]{x}+1/(\sqrt[4]{x)} ?

The integral of \sqrt[4]{x}+1/(\sqrt[4]{x)} is 4/5 x^{5/4}+4/3 x^{3/4}+C

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integral of \sqrt[4]{x}+1/(\sqrt[4]{x)}

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

\frac{4}{5} x^{\frac{5}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

Solution steps

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

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

\int \frac{1}{4 x} d x = \frac{4}{3} x^{\frac{3}{4}}

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

Add a constant to the solution

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

\int 5 x e^{- 2 x} d x

\frac{2}{s + 3}

\frac{s + 1}{( s ^{2} + 9 )}

f (x) = 2 x^{2} - 3 x - 2, at x = 6

\int_{- \infty}^{- 1} e^{- 4 t} d t

What is the integral of \sqrt[4]{x}+1/(\sqrt[4]{x)} ?
The integral of \sqrt[4]{x}+1/(\sqrt[4]{x)} is 4/5 x^{5/4}+4/3 x^{3/4}+C