What is the integral of 1/(x(ln(x))^{3/2)} ?

The integral of 1/(x(ln(x))^{3/2)} is -2/(ln^{1/2)(x)}+C

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integral of 1/(x(ln(x))^{3/2)}

\int \frac{1}{x ( ln ( x ) ) ^{\frac{3}{2}}} d x

- \frac{2}{ln ^{\frac{1}{2}} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{\frac{3}{2}}} d x

Simplify

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

Apply u-substitution

: \int \frac{1}{u ^{\frac{3}{2}}} d u

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

Apply the Power Rule

: - \frac{2}{u ^{\frac{1}{2}}}

= - \frac{2}{u ^{\frac{1}{2}}}

Substitute back

u = ln (x)

= - \frac{2}{ln ^{\frac{1}{2}} ( x )}

Add a constant to the solution

= - \frac{2}{ln ^{\frac{1}{2}} ( x )} + C

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What is the integral of 1/(x(ln(x))^{3/2)} ?
The integral of 1/(x(ln(x))^{3/2)} is -2/(ln^{1/2)(x)}+C