Question

高数不定积分求大佬帮帮忙？

如图所示，感觉像是用分部积分法，可是自己有些菜不会拆开。

Answer 1

(x^2+1)/(x+3)^2 = [(x+3)^2-(6x+8)]/(x+3)^2
= 1 - (6x+18-10)/(x+3)^2
= 1 - 6/(x+3) + 10/(x+3)^2
I = ∫e^xdx - 6∫e^xdx/(x+3) +10∫e^xdx/(x+3)^2
= e^x - 6∫e^xdx/(x+3) -10∫e^xd[1/(x+3)]
= e^x - 6∫e^xdx/(x+3) -10e^x/(x+3) +10∫e^xdx/(x+3)
= e^x -10e^x/(x+3) +4∫e^xdx/(x+3)
e^x/(x+3) 的原函数不是初等函数。请附印刷版原题。