由於列表比較長，積分表被分為以下幾個部分： 有理函式積分表 無理函式積分表 指數函式積分表 對數函式積分表 高斯函式積分表 三角函式積分表 反三角函式積分表 雙曲函式積分表 反雙曲函式積分表 含有 axb 的積分 int axbnmbox d xfrac axbn1a n1C intfrac 1axbmbox d xfrac 1aln left axbrightC intfrac xaxbmbox d xfrac 1a2axbblnleft axb right C intfrac x2axbmbox d xfrac 12a3 left axb24b axb2b2 lnleft axbright rightC intfrac 1x axbmbox d x frac 1blnleft frac axbxright C intfrac 1x2 axbmbox d xfrac ab2lnleft frac axbxright frac 1bxC 含有 sqrt abx 的積分 int xsqrt abxmbox d xfrac 215b23bx2aabxfrac 32C int x2sqrt abxmbox d xfrac 2105b315b2x212abx8a2abxfrac 32C int xnsqrt abxmbox d xfrac 2b 2n3 xn abxfrac 32 frac 2nab 2n3int xn1sqrt abxmbox d x intfrac sqrt abxxmbox d x2sqrt abxaintfrac 1xsqrt abxmbox d x intfrac sqrt abxxnmbox d xfrac 1a n1frac abxfrac 32xn1 frac 2n5 b2a n1intfrac sqrt abxxn1mbox d xnneq 1 intfrac 1xsqrt abxmbox d xfrac 1sqrt alnleft frac sqrt abx sqrt asqrt abxsqrt aright Ca0 frac 2sqrt aarctansqrtfrac abxa Ca0 intfrac xsqrt abxmbox d xfrac 2 abxfrac 323b2 frac 2asqrt abxb2 intfrac 1xnsqrt abxmbox d xfrac 1a n1frac sqrt abxxn1 frac 2n3 b2a n1intfrac 1xn1sqrt abxmbox d xnneq 1 含有 x2pmalpha2 的積分 intfrac 1x2alpha2mbox d xfrac arctandfrac xalphaalphaC intfrac 1pm x2mpalpha2mbox d x frac lnleft dfrac xmpalphapm xalpharight2alphaC 含有 ax2b 的積分 intfrac 1ax2bmbox d xfrac 1sqrt ab arctanfrac sqrt a xsqrt bC 含有 ax2bxc 的積分 int ax2bxcmbox d xfrac ax33frac bx22cxC 含有 sqrt a2x2qquad a0 的積分 intsqrt a2x2mbox d xfrac 12 xsqrt a2x2frac 12 a2lnleft xsqrt a2x2right C int x2sqrt a2x2mbox d xfrac 18 x a22x2sqrt a2x2frac 18 a4lnleft xsqrt a2x2right C int frac sqrt a2x2xmbox d x sqrt a2x2 aln left frac asqrt a2x2x right C int frac sqrt a2x2x2mbox d x lnleft xsqrt a2x2right frac sqrt a2x2x C int frac 1sqrt a2x2mbox d xln left xsqrt a2x2 right C intfrac x2sqrt a2x2mbox d xfrac 12 xsqrt a2x2 frac 12 a2lnleft sqrt a2x2x right C intfrac 1xsqrt a2x2mbox d xfrac 1alnleft frac xasqrt a2x2right C intfrac 1x2sqrt a2x2mbox d xfrac sqrt a2x2a2xC 含有 sqrt x2a2qquad x2a2 的積分 int frac 1sqrt x2a2mbox d xln xsqrt x2a2 C 含有 sqrt a2x2 qquad a2x2 的積分 intsqrt a2x2mbox d xfrac 12 xsqrt a2x2 frac a22arcsinfrac xaC int frac 1sqrt a2x2mbox d x arcsin frac xa C arccos frac xa C int x2sqrt a2x2mbox d xfrac 18 x 2x2a2sqrt a2x2 frac 18 a4arcsinfrac xaC intfrac sqrt a2x2xmbox d xsqrt a2x2 alnleft frac asqrt a2x2xright C intfrac sqrt a2x2x2mbox d xfrac sqrt a2x2x arcsinfrac xaC intfrac 1xsqrt a2x2mbox d xfrac 1alnleft frac asqrt a2x2xright C intfrac x2sqrt a2x2mbox d xfrac 12 xsqrt a2x2frac 12 a2arcsinfrac xaC intfrac 1x2sqrt a2x2mbox d xfrac sqrt a2x2a2xC 含有 Rsqrt ax2bxcqquad ane0 的積分 intfrac mbox d xR frac 1sqrt alnleft 2sqrt a R2axbrightqquad mbox for a0 intfrac mbox d xR frac 1sqrt aoperatorname arsinhfrac 2axbsqrt 4acb2 qquad mbox for a0mbox 4acb20mbox intfrac mbox d xR frac 1sqrt aln2axb quad mbox for a0mbox 4acb20mbox intfrac mbox d xR frac 1sqrt aarcsinfrac 2axbsqrt b24ac qquad mbox for a0mbox 4acb20mbox left 2axbrightsqrt b24acmbox intfrac mbox d xR3 frac 4ax2b4acb2 R intfrac mbox d xR5 frac 4ax2b3 4acb2 Rleft frac 1R2frac 8a4acb2right intfrac mbox d xR2n1 frac 22n14acb2left frac 2axbR2n14a n1intfrac mbox d xR2n1right intfrac xRmbox d x frac Rafrac b2aintfrac mbox d xR intfrac xR3mbox d x frac 2bx4c4acb2 R intfrac xR2n1mbox d x frac 12n1 aR2n1frac b2aintfrac mbox d xR2n1 intfrac mbox d xxRfrac 1sqrt clnleft frac 2sqrt c Rbx2cxright intfrac mbox d xxRfrac 1sqrt coperatorname arsinhleft frac bx2cxsqrt 4acb2right 含有三角函式的積分 intcos xmbox d xsin xC intsin xmbox d x cos xC intsec2xmbox d xtan xC intcsc2xmbox d xcot xC intsec xtan xmbox d xsec xC intcsc xcot xmbox d xcsc xC inttan xmbox d xln leftcos xrightCln leftsec xrightC intcot xmbox d xln leftsin xrightC intsec xmbox d xln leftsec xtan xrightC intcsc xmbox d xln leftcsc xcot xrightCln lefttan xsin xoversin xtan xrightC int sin n x mbox d x frac 1n sin n1 x cos x frac n1n int sin n2 x mbox d x C quad forall n ge 2 int sin 2 x mbox d x frac x2frac sin 2x4 C int cos n x mbox d x frac 1n cos n1 x sin x frac n1n int cos n2 x mbox d x C quad forall n ge 2 int cos 2 x mbox d x frac x2frac sin 2x4 C int tan n x mbox d x frac 1n1 tan n1 x int tan n2 x mbox d x C quad forall n ge 2 int tan 2 x mbox d x tan x x C int cot n x mbox d x frac 1n1 cot n1 x int cot n2 x mbox d x C quad forall n ge 2 int cot 2 x mbox d x cot x x C int sec n x mbox d x frac 1n1 sec n2 x tan x frac n2n1 int sec n2 x mbox d x C quad forall n ge 2 int csc n x mbox d x frac 1n1 csc n2 x cot x frac n2n1 int csc n2 x mbox d x C quad forall n ge 2 含有反三角函式的積分 int arcsin x mbox d x x arcsin x sqrt 1 x2 C int arccos x mbox d x x arccos x sqrt 1 x2 C int arctan x dx x arctan x frac 12 ln vert 1 x2 vert C int arccot x dx x arccot x frac 12 ln vert 1 x2 vert C int arcsec x mbox d x x arcsec x sgn xln leftx sqrt x2 1right C x arcsec x sgn xln leftx sqrt x2 1right C int arccsc x mbox d x x arccsc x sgn xln leftx sqrt x2 1right C x arccsc x sgn xln leftx sqrt x2 1right C 含有指數函式的積分 int exmbox d xexC intalphaxmbox d xfrac alphaxlnalphaC int xeaxmbox d xfrac 1a2ax1 eaxC int xneaxmbox d xfrac 1a xneaxfrac naint xn1 eaxmbox d x int eaxsin bx mbox d xfrac eaxa2b2asin bxbcos bxC int eaxcos bx mbox d xfrac eaxa2b2acos bxbsin bxC 含有對數函式的積分 intln xmbox d x xln x x C intlog_alpha xmbox d xfrac 1lnalphaleft xln x xrightC int xnln xmbox d x frac xn1n12n1ln x 1 C intfrac 1xln xmbox d x ln ln xC 含有雙曲函式的積分 int sinh x mbox d x cosh x C int cosh x mbox d x sinh x C int tanh x mbox d x lnleft cosh xright C int coth x mbox d x lnleftsinh xright C int mbox sech x mbox d x arcsinleft tanh xright C arctanleft sinh xright C int mbox csch x mbox d x lnlefttanh x over2right C 定積分 intinfty_infty ealpha x2mbox d xsqrt frac pialpha int_0frac pi2 mbox sinn xmbox d xint_0frac pi2 mbox cosn xmbox d x begin cases frac n1ncdotfrac n3n2cdotldotscdotfrac 45cdotfrac 23 mbox if n1mbox 且 nmbox 為 奇 數 frac n1ncdotfrac n3n2cdotldotscdotfrac 34cdotfrac 12cdotfrac pi2 mbox if n0mbox 且 nmbox 為 偶 數 end cases 這是沃利斯公式的一個情形，詳見沃利斯乘積 Category 微積分 Category 數學列表 Category 數學恆等式