What is the integral of (sqrt(2))/(x^2sqrt(x)) ?

The integral of (sqrt(2))/(x^2sqrt(x)) is -(2sqrt(2))/(3x^{3/2)}+C

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integral of (sqrt(2))/(x^2sqrt(x))

\int \frac{2}{x ^{2} x} d x

- \frac{2 2}{3 x ^{\frac{3}{2}}} + C

Solution steps

\int \frac{2}{x ^{2} x} d x

Take the constant out:

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

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

Simplify

x^{2} x : x^{\frac{5}{2}}

= 2 \cdot \int \frac{1}{x ^{\frac{5}{2}}} d x

Apply the Power Rule

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

= 2 (- \frac{2}{3 x ^{\frac{3}{2}}})

Simplify

2 (- \frac{2}{3 x ^{\frac{3}{2}}}) : - \frac{2 2}{3 x ^{\frac{3}{2}}}

= - \frac{2 2}{3 x ^{\frac{3}{2}}}

Add a constant to the solution

= - \frac{2 2}{3 x ^{\frac{3}{2}}} + C

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What is the integral of (sqrt(2))/(x^2sqrt(x)) ?
The integral of (sqrt(2))/(x^2sqrt(x)) is -(2sqrt(2))/(3x^{3/2)}+C