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

The integral of (ln(x))/(x^{3/2)} is -(2ln(x))/(x^{1/2)}-4/(x^{1/2)}+C

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

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

- \frac{2 ln ( x )}{x ^{\frac{1}{2}}} - \frac{4}{x ^{\frac{1}{2}}} + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{2}{x ^{\frac{3}{2}}} d x = \frac{4}{x ^{\frac{1}{2}}}

= - \frac{2 ln ( x )}{x ^{\frac{1}{2}}} - \frac{4}{x ^{\frac{1}{2}}}

Add a constant to the solution

= - \frac{2 ln ( x )}{x ^{\frac{1}{2}}} - \frac{4}{x ^{\frac{1}{2}}} + C

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What is the integral of (ln(x))/(x^{3/2)} ?
The integral of (ln(x))/(x^{3/2)} is -(2ln(x))/(x^{1/2)}-4/(x^{1/2)}+C