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

The integral from 1 to infinity of (ln(x))/(x^{3/2)} is 4

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

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

4

Solution steps

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

Compute the indefinite integral:

\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

Compute the boundaries:

\int_{1}^{\infty} \frac{ln ( x )}{x ^{\frac{3}{2}}} d x = 0 - (- 4)

= 0 - (- 4)

Simplify

= 4

What is the integral from 1 to infinity of (ln(x))/(x^{3/2)} ?
The integral from 1 to infinity of (ln(x))/(x^{3/2)} is 4