Confused with integral and natural logarithm

When reading about ideal gas and adiabatic expansion, I got stuck with the following:

$${W}_{ab}={\int}_{{\mathit{V}}_{\mathit{a}}}^{{\mathit{V}}_{\mathit{b}}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\frac{dV}{{V}^{\alpha}}=\frac{{V}_{b}^{1-\alpha}-{V}_{a}^{1-\alpha}}{1-\alpha}$$

I know the following rule, but I couldn't come to the above:

$${\int}_{{\mathit{V}}_{\mathit{a}}}^{{\mathit{V}}_{\mathit{b}}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\frac{dV}{V}=ln|\frac{{V}_{b}}{{V}_{a}}|$$

When reading about ideal gas and adiabatic expansion, I got stuck with the following:

$${W}_{ab}={\int}_{{\mathit{V}}_{\mathit{a}}}^{{\mathit{V}}_{\mathit{b}}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\frac{dV}{{V}^{\alpha}}=\frac{{V}_{b}^{1-\alpha}-{V}_{a}^{1-\alpha}}{1-\alpha}$$

I know the following rule, but I couldn't come to the above:

$${\int}_{{\mathit{V}}_{\mathit{a}}}^{{\mathit{V}}_{\mathit{b}}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\frac{dV}{V}=ln|\frac{{V}_{b}}{{V}_{a}}|$$