Lös 1 ∫ (from a to b) of 1/x wrt x

$$1 \int _ { a } ^ { b } \frac { 1 } { x } d x$$

Beräkna

$$\left\{\begin{matrix}\text{Indeterminate},&\left(a>0\text{ and }b<0\right)\text{ or }\left(b>0\text{ and }a<0\right)\\\ln(|b|)-\ln(|a|),&\left(a>0\text{ and }a<b\right)\text{ or }\left(b<0\text{ and }a<b\right)\text{ or }b=a\\\infty,&\left(b=0\text{ and }a>0\right)\text{ or }\left(a=0\text{ and }b>0\right)\\-\infty,&\left(a=0\text{ and }b<0\right)\text{ or }\left(b=0\text{ and }a<0\right)\\\ln(|a|)-\ln(|b|),&\left(b>0\text{ or }a<0\right)\text{ and }b<a\end{matrix}\right,$$

Derivera m.a.p. a

$$\text{Indeterminate}$$