令x=√2tanα,0≤α≤π/4，∫dx/√(2+x^2)=∫d(√2tanα)/√2secα=∫dtanα/secα=∫cosαdα/cos^2α=∫dsinα/(1-sinα)(1+sinα)=(1/2)[∫dsinα/(1-sinα)+∫dsinα/(1+sinα)]=(1/2)*[-ln(1-sinα)+ln(1+sinα)]+C=ln(tanα+secα)+C
