∫ [(x^3-2x^2+x+1)/(x^4+5x^2+4)]dx (x的3次方-2*x的朋友+x+1)/(x的四次方+5*x的平_数学解答

∫ [(x^3-2x^2+x+1)/(x^4+5x^2+4)]dx
(x的3次方-2*x的朋友+x+1)/(x的四次方+5*x的平方+4)

人气：465 ℃　时间：2020-06-06 17:56:28

解答

[(x^3-2x^2+x+1)/(x^4+5x^2+4)]
=1/(x^2+1)+(x-3)/(x^2+4).
原式=∫1/(x^2+1)dx+∫(x-3)/(x^2+4)dx
=arctanx+(1/2)ln(x^2+4)-(3/2)arctan(x/2)+C.