∫(0->π/2) dx/(sinx+cosx) =(1/√2)∫(0->π/2) dx/sin(x+π/4) =(1/√2)∫(0->π/2) csc(x+π/4) dx =(1/√2) ln|csc(x+π/4) - cot(x+π/4)| | (0->π/2) =(1/√2) [ ln|√2 +1| - ln|√2-1| ] =(1/√2)ln(3+2√2)
