1
Calculer \(\int_{t=0}^{\pi/4} \ln(1+\tan t)\,d t\). On remarquera que \(\cos t + \sin t = \sqrt 2 \cos\left(\frac \pi4 - t\right)\).
Calculer \(\int_{t=0}^{\pi/4} \ln(1+\tan t)\,d t\). On remarquera que \(\cos t + \sin t = \sqrt 2 \cos\left(\frac \pi4 - t\right)\).