求(x^4-1)/(x^4+1)的不定积分,
问题描述：
求(x^4-1)/(x^4+1)的不定积分,
答
原式=∫[1-2/(x^4+1)] dx而1/(x^4+1)=1/4*(2-√2x)/(x^2-√2x+1)+1/4*(2+√2x)/(x^2+√2x+1)逐项积分,结果=1/(2√2)*ln(x^2-√2x+1)-1/(2√2)*ln(x^2+√2x+1)+1/√2*arctan(1-√2x)-1/√2*arctan(1+√2x)+x+C...