大一高等数学不定积分题目

Question

大一高等数学不定积分题目急求

Answer 1

如图

追问

谢啦

佩服佩服

Answer 2

∫((x^11)/(x^8+3x^4+2))dx
=1/4·∫((x^8)/(x^8+3x^4+2))d(x^4)
=1/4·x^4-1/4·∫((3x^4+2)/(x^4+1)(x^4+2))d(x^4)
=1/4·x^4+1/4·∫1/(x^4+1)d(x^4)-∫1/(x^4+2)d(x^4)
=1/4·x^4+ln(((x^4+1)^(1/4))/(x^4+2))+C

Answer 3

差不多这样

再代回去就可以

Answer 4

先设 x^4=t 原式 =>1/4∫t^2/(t^2+3t+2) dt
=>1/4∫(1- (3t+2)/(t^2+3t+2))dt
=>1/4∫(1- (-1/(t+1)+4/(t+2)))dt
后面自己算吧 电脑打字麻烦