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

The integral of ((x+1)/(\sqrt[4]{x)}) is 4/7 x^{7/4}+4/3 x^{3/4}+C

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

\frac{4}{7} x^{\frac{7}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

Solution steps

Expand

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{3}{4}} d x = \frac{4}{7} x^{\frac{7}{4}}

= \frac{4}{7} x^{\frac{7}{4}} + \frac{4}{3} x^{\frac{3}{4}}

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

What is the integral of ((x+1)/(\sqrt[4]{x)}) ?
The integral of ((x+1)/(\sqrt[4]{x)}) is 4/7 x^{7/4}+4/3 x^{3/4}+C