∫dx/(1+x^4) 　　=(1/2)∫[(1+x^2)+(1-x^2)]/(1+x^4)dx,乘以2除以2 　　=(1/2)∫(1+x^2)/(1+x^4)dx+(1/2)∫(1-x^2)/(1+x^4)dx 　　=(1/2)∫(1/x^2+1)/(1/x^2+x^2)dx+(1/2)∫(1/x^2-1)/(1/x^2+x^2)dx,分子分母除以x^2 　　=(1/2)∫d(x-1/x)/[(x-1/x)²+2]-(1/2)∫d(1/x+x)/[(x+1/x)²-2] 　　=(1/2)*(1/√2)arctan[(x-1/x)/√2]-(1/2)*(1/2√2)ln|(x+1/x-√2)/(x+1/x+√2)|+C 　　=1/(2√2)*arctan[x/√2-1/(√2x)]-1/(4√2)ln|(x²-√2x+1)/(x²+√2x+1)|+C 　　公式1：∫dx/(x²+a²)=(1/a)arctan(x/a) 　　公式2：∫dx/(x²-a²)=1/(2a)*ln|(x-a)/(x+a)|