∫ 1/x(x^4+1)dx=

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/22 00:01:00

∫ 1/x(x^4+1)dx=

let
x^2= tany
2xdx = (secy)^2 dy
∫dx/[x(x^4+1)]
=∫(2xdx)/[x^2(x^4+1)]
=∫(secy)^2 dy/[tany(secy)^2]
=∫coty dy
=ln|siny| + C
=ln |x^2/√(x^4+1)| + C

∫（x^2+1/x^4)dx ∫X^4/1+x dx. ∫dx/x(1+x^4) ∫1/(x^4-x^2)dx ∫1/√x*(4-x)dx ∫dx/[x√(1-x^4)] ∫ x/(1+X^2)dx= ∫dx/x(1+x) ∫1/(1-x^4)dx=? ∫(x^4-4x^2+5x-15)/(x^2+1)(x-2) dx=? ∫ 1/x(x^4+1)dx= ∫(1-x)/[√(9-4x^2)]dx=