Tentukan integral log(sinx+cosx) dari -pi/4 ke pi/4.
(I = int_{-pi/4}^{pi/4}log(sinx+cosx)dx) (I = int_{-pi/4}^{pi/4}log[sqrt{2} ]*[frac{1}{sqrt{2}}sinx+frac{1}{sqrt{2}}cosx]=int_{-pi/4}^{pi/4}log(sqrt{2}sin[x +pi/4])dx)
Masukkan x+π/4=t
(I = int_{0}^{pi/2}log[sqrt{2}]sintdt=int_{0}^{pi/2}log(sqrt{2}+log sintdt=logsqrt{2}int_ {0}^{pi/2}1dt+int_{0}^{pi/2}log sintdt=pi/2 logsqrt{2}-pi/2 log2=-pi/4 log2)