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

Lösung

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

4

Schritte zur Lösung

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

Berechne das unbestimmte 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

Berechne die Grenzen:

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

= 0 - (- 4)

Vereinfache

= 4

\frac{d}{d x} (1000 (1 + \frac{x}{12})^{60})

d er i v a t i v e f (x) = (1 - x) (x^{2} - 7)^{2}

in v erse l a pl a ce \frac{10}{s ( s ^{2} + 8 s + 25 )}

\frac{\partial}{\partial x} (x arctan (yz))

x \to 0 lim (\frac{sin ( \frac{x}{2} )}{x})