Soit \(\gamma\) la constante d’Euler. Montrer que …
1
\(\int_{t=0}^{+\infty} e^{-t}\ln t\,d t = -\gamma\).
2
\(\int_{t=0}^1 \frac{1-e^{-t}-e^{-1/t}}t\,d t = \gamma\).
3
\(\int_{t=0}^1 \left(\frac 1t + \frac 1{\ln(1-t)}\right)d t = \gamma\).
Soit \(\gamma\) la constante d’Euler. Montrer que …
\(\int_{t=0}^{+\infty} e^{-t}\ln t\,d t = -\gamma\).
\(\int_{t=0}^1 \frac{1-e^{-t}-e^{-1/t}}t\,d t = \gamma\).
\(\int_{t=0}^1 \left(\frac 1t + \frac 1{\ln(1-t)}\right)d t = \gamma\).