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

The integral of 1/(sqrt(x*\sqrt[4]{x))} is 8/3 x^{3/8}+C

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

\frac{8}{3} x^{\frac{3}{8}} + C

Solution steps

Apply u-substitution

: \int 4 u d u

= \int 4 u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int u d u

Apply the Power Rule

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

= 4 \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

Simplify

= \frac{8}{3} x^{\frac{3}{8}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{8}} + C

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What is the integral of 1/(sqrt(x*\sqrt[4]{x))} ?
The integral of 1/(sqrt(x*\sqrt[4]{x))} is 8/3 x^{3/8}+C