常用积分表.pdf

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1、常用积分公式（一）含有axb+的积分(a≠0)dx11．∫＝lnaxb++Cax+baμ1μ+12．∫()axb+dx＝()axb++C（μ≠−1）a(1μ+)x13．dx＝(lax+bb−+naxb)+C∫2axb+a2x11⎡⎤224．dx＝()ax+b−+2bax()lb++bnaxb+C∫axb+3⎢⎥a⎣⎦2dx1ax+b5．∫＝−ln+Cx()ax+bbxdx1aaxb+6．＝−++lnC∫22x()ax+bbxbxx1b7．dx＝(lnax++b)+C∫22()ax+baax+b22x1b8．dx

2、＝(2axb+−+blnaxb−)+C∫23()axb+aax+bdx11ax+b9．＝−+lnC∫22x()axb+baxb()+bx（二）含有axb+的积分2310．∫ax+bxd＝()ax++bC3a2311．xax+bxd＝(3ax−2)(bax++b)C∫215a22222312．xax+bxd＝(15ax−+12abx8b)(ax+b)+C∫3105ax213．dx＝(2ax−+b)axb+C∫2axb+3a12x222214．dx＝(3ax−4abx++8)baxb+C∫3axb+15a⎧1ax+

3、−bb⎪ln+Cb(>0)dx⎪bax++bb15．∫＝⎨xax+b⎪+2axb⎪arctan+Cb(<0)⎩−b−bdxax+badx16．∫2＝−−∫xaxb+bx2bxax+bax+bdx17．∫dx＝2axb++b∫xxaxb+ax+bax+badx18．dx＝−+∫2∫xx2xax+b22（三）含有x±a的积分dx1x19．=arctan+C∫22x+aaadxxn23−dx20．=+∫22n2221nn−−2∫221()x+a2(naxa−+1)()2(naxa−+1)()dx1xa−21．=ln+

4、C∫22x−a2axa+2（四）含有ax+>ba(0)的积分⎧1a⎪arctanxC+>(b0)dx⎪abb22．＝⎨∫2ax+b⎪1ax−−bln+Cb(<0)⎪⎩2−+abax−bx1223．dx＝lnax++bC∫2ax+b2a22xxbxd24．dx＝−∫2∫2ax+baaaxb+2dx1x25．＝ln+C∫22x()ax+b2bax+bdx1dax26．＝−−∫22∫2x()ax+bbxbax+b2dxaax+b127．＝ln−+C∫32222x()ax+b22bxbxdxx1dx28．＝+∫2222

5、∫()ax+b2(bax++b)2baxb2（五）含有ax++bxc(0a>)的积分⎧22axb+2arctan+Cba(4c)⎪ba22−+42caxbba+−4c⎩x1d2bx30．dx＝lnax++−bxc∫2∫2ax++bxc22aaax+bx+c22（六）含有x+a(0a>)的积分dxx2231．＝arsh+C＝ln(x+++xaC)∫22a1x+adxx32．∫＝+C223222()xa

6、+axa+x2233．∫dx＝x+aC+22xa+x134．∫dx＝−+C22322()xa+xa+322xxa222235．∫dx＝x+−axln(+++xa)Cxa22+222xx2236．∫dx＝−++++ln(xxaC)22322()xa+xa+22dx1xaa+−37．∫＝ln+Cxxa22+ax22dxxa+38．＝−+C∫222ax2xxa+222xa222239．∫x+axd＝x++axln(+++xa)C22223x2222432240．∫()x+axd＝(2x+5)axaaxxaC++ln(

7、+++)8822122341．∫xxa+dx＝()x++aC34222xa22222242．∫xxa+dx＝(2x+axa)+−ln(xxaC+++)882222xa+22xaa+−43．∫dx＝x+aa++lnCxx2222xa+xa+2244．dx＝−++++ln(xxaC)∫2xx22（七）含有x−a(0a>)的积分dxxx2245．＝arch+C=lnx+−+xaC∫22xa1x−adxx46．∫＝−+C223222()x−aaxa−x2247．∫dx＝x−aC+22xa−4x148．∫dx＝−+C22

8、322()xa−xa−22xxa222249．∫dx＝x−+axln+−+xaCxa22−222xx2250．∫dx＝−++−+lnxxaC22322()xa−xa−dx1a51．∫＝arccos+Cxxa22−ax22dxxa−52．＝+C∫222ax2xxa−222xa222253．∫x−axd＝x−−axln+−+xaC22223x2222432254．∫()x−axd＝(2x−