令x=tany，dx=sec²y dy(1+x²)^(-3/2)=1/(1+tan²y)^(3/2)=1/(sec²y)^(3/2)=1/sec³y=cos³y∴原式=∫cos³y*sec²y dy=∫cos³y*1/cos²y dy=∫cosy dy=siny + C=x/√(1+x²) + C，C为任意常数
