Question

高等数学，不定积分

高等数学，不定积分题目如图，请问这个不定积分如何求解？？谢谢各位老师指点！！

Answer 1

∫dx/(1+x^4) = (1/2)∫[(x^2+1)-(x^2-1)]dx/(x^4+1)
= (1/2) [∫(1+1/x^2)dx/(x^2+1/x^2) - ∫(1-1/x^2)dx/(x^2+1/x^2)]
= (1/2) {∫d(x-1/x)/[x-1/x)^2+2] - ∫d(x+1/x)/[x+1/x)^2-2]}
= (√2/4)arctan[(x^2-1)/(√2x)] - (√2/8)ln|(x^2+1-√2x)/(x^2+1+√2x)| + C