1+x^4=(1+x²)²-2x²=(1+x²+√2x)(1+x²-√2x)1/(1+x^4)=[1/(1+x²-√2x)-1/(1+x²+√2x)]/2√2x=1/2√2*[1/x+(√2-x)/(1+x²-√2x)-1/x+(√2+x)/(1+x²+√2x)]=1/4√2*[(2x+2√2)/(x²+√2x+1)-(2x-2√2)/(x²+1-√2x)]=1/4√2*[(2x+√2)/(x²+√2x+1)-(2x-√2)/(x²+1-√2x)+√2/(x²+√2x+1)+√2/(x²+1-√2x)]对(2x+√2)/(x²+√2x+1)求积分得ln(x²+√2x+1)对(2x-√2)/(x²+1-√2x)求积分得ln(x²+1-√2x)对√2/(x²+√2x+1)求积分得2arctan(√2x+1)对√2/(x²-√2x+1)求积分得2arctan(√2x-1)原式=1/4√2*{ln[(x²+√2x+1))/(x²+1-√2x)]+2arctan(√2x+1)+2arctan(√2x-1)}+C