$\ln |x + c| $ ?

0 votes

Let $0 < \alpha < \beta < 1$. Then $$ \Sigma_{k=1}^{\infty} \int_{1/(k+\beta)}^{1/(k+\alpha)} \frac{1}{1+x} dx$$ is equal to

- $\log_e \frac{\beta}{\alpha}$
- $\log_e \frac{1+ \beta}{1 + \alpha}$
- $\log_e \frac{1+\alpha }{1+ \beta}$
- $\infty$