∫(0,1) dx/[(x+1)√(x^2+1)]
令x=tant dx=sec^2tdt
原式=∫(0,π/4) sec^2tdt/[(tant+1)*sect]
=∫(0,π/4) dt/(sint+cost)
=∫(0,π/4) dt/[√2*sin(t+π/4)]
=(1/√2)*∫(0,π/4) csc(t+π/4)*d(t+π/4)
=(1/√2)*ln[csc(t+π/4)-ctg(t+π/4)]|(0,π/4)
=(1/√2)*[ln1-ln(√2-1)]
=(1/√2)*ln(√2+1)