What is the integral of 1/(sqrt(x\sqrt{x))} ?

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

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integral of 1/(sqrt(x\sqrt{x))}

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

4 4 x + C

Solution steps

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

Simplify

x x : x^{\frac{3}{2}}

= \int \frac{1}{x ^{\frac{3}{2}}} d x

x^{\frac{3}{2}} = x^{\frac{3}{4}},

assuming

x \geq 0

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

Apply the Power Rule

: 4 x^{\frac{1}{4}}

= 4 x^{\frac{1}{4}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 4 4 x

Add a constant to the solution

= 4 4 x + C

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