a=1+e^xx=ln(a-1)dx=1/(a-1) da原式=∫(1/a²)*1/(a-1) da=∫[(-1/2)(1/a)-(1/2)(1/a²)+(1/2)*1/(a-1)]da=-1/2*lna+1/(2a)+1/2*ln(a-1)+C=-1/2*ln(1+e^x)+1/(2+2e^x)+x/2+C
