Question

定积分∫1 0(x/(1+x^2))dx

Answer 1

∫(0→1)x/(1+x²)dx= ½∫(0→1)dx²/(1+x²)= ½∫(0→1)d(1+x²)/(1+x²)= ln(1+x²) (0→1)= ½[ln2 - ln1]= ½ln2≈ 0.3466