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

The integral of (x+1)/(\sqrt[4]{x)}(x-1) is 4/11 x^{11/4}-4/3 x^{3/4}+C

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

\frac{4}{11} x^{\frac{11}{4}} - \frac{4}{3} x^{\frac{3}{4}} + C

Solution steps

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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{7}{4}} d x = \frac{4}{11} x^{\frac{11}{4}}

= \frac{4}{11} x^{\frac{11}{4}} - \frac{4}{3} x^{\frac{3}{4}}

Add a constant to the solution

= \frac{4}{11} x^{\frac{11}{4}} - \frac{4}{3} x^{\frac{3}{4}} + C

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What is the integral of (x+1)/(\sqrt[4]{x)}(x-1) ?
The integral of (x+1)/(\sqrt[4]{x)}(x-1) is 4/11 x^{11/4}-4/3 x^{3/4}+C