常用的函数积分表(增强版)

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1、1.fx+gxdx=fxdx+gxdx2.fx-gxdx=fxdx-gxdx3.fxdgx=fxgx-gxdfx4.axdx=axlna+C，a≠1，a>05.xndx=xn+1n+1+C，n≠-16.1xdx=lnx+C7.exdx=ex+C8.sinxdx=-cosx+C9.cosxdx=sinx+C10.sec2xdx=tanx+C11.csc2xdx=-cotx+C12.secxtanxdx=secx+C13.cscxcotxdx=-cscx+C14.ax+bndx=ax+bn+1an+1+C，a≠0，n≠-11

2、5.dxax+b=1alnax+b+C，a≠016.xax+bndx=ax+bn+1a2ax+bn+2-bn+1+C，a≠0，n≠-1,-217.xax+bdx=xa-ba2lnax+b+C，a≠018.xax+b2dx=1a2lnax+b+bax+b+C，a≠019.x2ax+bdx=12a3ax+b2-4bax+b+2b2lnax+b+C20.x2ax+b2dx=1a3ax+b-2blnax+b-b2ax+b+C21.x2ax+b3dx=1a3lnax+b+2bax+b-b22ax+b2+C211.x2ax+bndx

3、=1a3-1n-3ax+bn-3+2bn-2ax+bn-2-b2n-1ax+bn-1+C，n≠1,2,32.dxxax+b=1blnxax+b+C，b≠03.dxx2ax+b=-1bx+ab2lnax+bx+C4.dxx2ax+b2=-a1b2ax+b+1ab2x-2b3lnax+bx+C5.xax+bdx=215a23ax-2bax+b32+C6.x2ax+bdx=2105a315a2x2-12abx+8b2ax+b32+C7.ax+bndx=2ax+bn+2an+2+C，a≠0，n≠-28.xnax+bdx=2a2n

4、+3xnax+b32-2nba2n+3xn-1ax+bdx循环计算9.ax+bxdx=2ax+b+bdxxax+b=2ax+b-2barctanhax+bb+C10.dxxax+b=2-barctanax+b-b+C，b<011.dxxax+b=1blnax+b-bax+b+b+C，b>012.ax+bx2dx=-ax+bx+a2dxxax+b+C13.ax+bxndx=-ax+b32bn-1xn-1-2n-5a2bn-1ax+bxn-1dx，n≠1循环计算14.xnax+bdx=2a2n+1xnax+b-bnxn-1a

5、x+b+C循环计算211.dxx2ax+b=-ax+bbx-a2bdxxax+b+C，b≠02.dxxnax+b=-ax+bbn-1xn-1-2n-3a2bn-1ax+bxn-1dx，n≠1循环计算3.xnax+bdx=22n+1xn+1ax+b+bxnax+b-nbxn-1ax+bdx+C循环计算4.dxa2+x2=1aarctanxa+C，a≠05.dxa2+x22=x2a2a2+x2+12a3arctanxa+C，a≠06.dxa2-x2=12alna+xa-x+C=1aarctanhxa+C，a≠0，a>x7.d

6、xa2-x22=x2a2a2-x2+14a3lnx+ax-a+C8.1x2-a2dx=12alnx-ax+a+C=-1aarccothxa+C，a≠0，x>a9.dxa2+x2=lnx+a2+x2+C10.a2+x2dx=x2a2+x2+a22lnx+a2+x2+C11.a2+x23dx=xa2+x234+38a2xa2+x2+38a4lnx+a2+x2+C12.a2+x25dx=xa2+x256+524a2xa2+x23+516a4xa2+x2+516a6lnx+a2+x2+C13.xa2+x22n+1dx=a2+x2

7、2n+32n+3+C14.x2a2+x2dx=x8a2+2x2a2+x2-a48lnx+a2+x2+C15.x2a2+x23dx=xa2+x256-a2xa2+x224-a4xa2+x216-a616lnx+a2+x2+C211.x3a2+x2dx=a2+x255-a2a2+x233+C2.x3a2+x23dx=a2+x277-a2a2+x255+C3.x3a2+x22n+1dx=a2+x22n+52n+5-a2a2+x22n+32n+3+C4.x4a2+x2dx=x3a2+x236-a2xa2+x238+a4xa2+x

8、216+a616lnx+a2+x2+C5.x4a2+x23dx=x3a2+x258-a2xa2+x2516+a4xa2+x2364+3a6xa2+x2128+3a8128lnx+a2+x2+C6.x5a2+x2dx=a2+x277-2a2a2+x255+a4a2+x233+C7.x5a2+x23dx=a2+x299-