Question

这道不定积分怎么解 希望老师写下较详细的过程

∫1/[x*(x^6+4)]dx 这道不定积分怎么解 希望老师写下较详细的过程 先谢谢老师们了

Answer 1

∫1/[x*(x^6+4)]dx =1/4∫[(4+x^6)-x^6]/[x*(x^6+4)]dx =1/4[∫1/xdx-∫x^5/(x^6+4)dx]=1/4{lnx-1/6∫dx^6/(x^6+4)}=1/4lnx-1/24ln(x^6+4)

Answer 2

∫1/[x*(x^6+4)]dx =1/4∫[(4+x^6)-x^6]/[x*(x^6+4)]dx =1/4[∫1/xdx-∫x^5/(x^6+4)dx]=1/4{lnx-1/6∫dx^6/(x^6+4)}=1/4lnx-1/24ln(x^6+4) 嘿嘿，可以给我加分了吧！！