以下是部份三角函式的積分表（省略積分常數）： 積分只有 sin 的函式 intsin cxdx frac 1ccos cx intsinn cxdx frac 1nc sinn1 cxcos cx frac n1nintsinn2 cxdx qquad 其中 n0 intsqrt 1 sin xdx intsqrt operatorname cvsxdx 2 frac cos frac x2 sin frac x2cos frac x2 sin frac x2 sqrt operatorname cvsx 2sqrt 1 sin x（其中 operatorname cvsx 是 餘矢 Coversine 函式 參閱正矢 versine 函式） int xsin cxdx frac sin cxc2frac xcos cxc int xnsin cxdx frac xnccos cxfrac ncint xn1cos cxdx qquad 其中 n0 int_frac a2frac a2 x2sin2 frac npi xadx frac a3 n2pi2624n2pi2 qquad 其中 n246 intfrac sin cxx dx sum_i0infty 1ifrac cx2i12i1cdot 2i1 intfrac sin cxxn dx frac sin cxn1 xn1 frac cn1intfrac cos cxxn1 dx intfrac dxsin cx frac 1cln lefttanfrac cx2right intfrac dxsinn cx frac cos cxc 1n sinn1 cxfrac n2n1intfrac dxsinn2 cx qquad 其中 n1 intfrac dx1pmsin cx frac 1ctanleft frac cx2mpfrac pi4right intfrac xdx1sin cx frac xctanleft frac cx2 frac pi4rightfrac 2c2lnleftcosleft frac cx2frac pi4rightright intfrac xdx1sin cx frac xccotleft frac pi4 frac cx2rightfrac 2c2lnleftsinleft frac pi4frac cx2rightright intfrac sin cxdx1pmsin cx pm xfrac 1ctanleft frac pi4mpfrac cx2right intsin c_1xsin c_2xdx frac sin c_1c_2 x2 c_1c_2frac sin c_1c_2 x2 c_1c_2 qquad 其中 c_1neqc_2 積分只有 cos 的函式 intcos cxdx frac 1csin cx intcosn cxdx frac 1nc cosn1 cxsin cx frac n1nintcosn2 cxdx qquadmbox n0mbox int xcos cxdx frac cos cxc2 frac xsin cxc int xncos cxdx frac xnsin cxc frac ncint xn1sin cxdx int_frac a2frac a2 x2cos2 frac npi xadx frac a3 n2pi2624n2pi2 qquadmbox n135mbox intfrac cos cxx dx lncxsum_i1infty 1ifrac cx2i2icdot 2i intfrac cos cxxn dx frac cos cxn1 xn1frac cn1intfrac sin cxxn1 dx qquadmbox nneq 1mbox intfrac dxcos cx frac 1clnlefttanleft frac cx2frac pi4rightright intfrac dxcosn cx frac sin cxc n1 cosn1 cx frac n2n1intfrac dxcosn2 cx qquadmbox n1mbox intfrac dx1cos cx frac 1ctanfrac cx2 intfrac dx1cos cx frac 1ccotfrac cx2 intfrac xdx1cos cx frac xctanfrac cx2 frac 2c2lnleftcosfrac cx2right intfrac xdx1cos cx frac xccotfrac cx2frac 2c2lnleftsinfrac cx2right intfrac cos cxdx1cos cx x frac 1ctanfrac cx2 intfrac cos cxdx1cos cx xfrac 1ccotfrac cx2 intcos c_1xcos c_2xdx frac sin c_1c_2 x2 c_1c_2frac sin c_1c_2 x2 c_1c_2 qquadmbox c_1neqc_2mbox 積分只有 tan 的函式 inttan cxdx frac 1clncos cx frac 1clnsec cx inttann cxdx frac 1c n1tann1 cxinttann2 cxdx qquadmbox for nneq 1mbox intfrac dxtan cx 1 frac x2 frac 12clnsin cx cos cx intfrac dxtan cx 1 frac x2 frac 12clnsin cx cos cx intfrac tan cxdxtan cx 1 frac x2 frac 12clnsin cx cos cx intfrac tan cxdxtan cx 1 frac x2 frac 12clnsin cx cos cx 積分只有 sec 的函式 int sec cx dx frac 1cln left sec cx tan cxright intsec2xmbox d xtan xC int secn cx dx frac secn2cx tan cxc n1 frac n2n1int secn2cx dx qquad mbox for n ne 1mbox int frac dxsec x 1 x tan frac x2 積分只有 csc 的函式 int csc cx dx frac 1cln left csc cx cot cxright intcsc2xmbox d xcot xC int cscn cx dx frac cscn2cx cot cxc n1 frac n2n1int cscn2cx dx qquad mbox for n ne 1mbox 積分只有 cot 的函式 intcot cxdx frac 1clnsin cx intcotn cxdx frac 1c n1cotn1 cx intcotn2 cxdx qquadmbox for nneq 1mbox intfrac dx1 cot cx intfrac tan cxdxtan cx1 intfrac dx1 cot cx intfrac tan cxdxtan cx1 積分只有 sin 和 cos 的函式 intfrac dxcos cxpmsin cx frac 1csqrt 2lnlefttanleft frac cx2pmfrac pi8rightright intfrac dxcos cxpmsin cx2 frac 12ctanleft cxmpfrac pi4right intfrac dxcos x sin xn frac 1n1left frac sin x cos xcos x sin xn 1 2 n 2intfrac dxcos x sin xn2 right intfrac cos cxdxcos cx sin cx frac x2 frac 12clnleftsin cx cos cxright intfrac cos cxdxcos cx sin cx frac x2 frac 12clnleftsin cx cos cxright intfrac sin cxdxcos cx sin cx frac x2 frac 12clnleftsin cx cos cxright intfrac sin cxdxcos cx sin cx frac x2 frac 12clnleftsin cx cos cxright intfrac cos cxdxsin cx 1cos cx frac 14ctan2frac cx2frac 12clnlefttanfrac cx2right intfrac cos cxdxsin cx 1cos cx frac 14ccot2frac cx2frac 12clnlefttanfrac cx2right intfrac sin cxdxcos cx 1sin cx frac 14ccot2left frac cx2frac pi4rightfrac 12clnlefttanleft frac cx2frac pi4rightright intfrac sin cxdxcos cx 1sin cx frac 14ctan2left frac cx2frac pi4rightfrac 12clnlefttanleft frac cx2frac pi4rightright intsin cxcos cxdx frac 12csin2 cx intsin c_1xcos c_2xdx frac cos c_1c_2 x2 c_1c_2frac cos c_1c_2 x2 c_1c_2 qquadmbox forc_1neqc_2mbox intsinn cxcos cxdx frac 1c n1sinn1 cx qquadmbox for nneq 1mbox intsin cxcosn cxdx frac 1c n1cosn1 cx qquadmbox for nneq 1mbox intsinn cxcosm cxdx frac sinn1 cxcosm1 cxc nmfrac n1nmintsinn2 cxcosm cxdx qquadmbox for mn0mbox also intsinn cxcosm cxdx frac sinn1 cxcosm1 cxc nm frac m1nmintsinn cxcosm2 cxdx qquadmbox for mn0mbox intfrac dxsin cxcos cx frac 1clnlefttan cxright intfrac dxsin cxcosn cx frac 1c n1cosn1 cxintfrac dxsin cxcosn2 cx qquadmbox for nneq 1mbox intfrac dxsinn cxcos cx frac 1c n1sinn1 cxintfrac dxsinn2 cxcos cx qquadmbox for nneq 1mbox intfrac sin cxdxcosn cx frac 1c n1cosn1 cx qquadmbox for nneq 1mbox intfrac sin2 cxdxcos cx frac 1csin cxfrac 1clnlefttanleft frac pi4frac cx2rightright intfrac sin2 cxdxcosn cx frac sin cxc n1cosn1 cxfrac 1n1intfrac dxcosn2 cx qquadmbox for nneq 1mbox intfrac sinn cxdxcos cx frac sinn1 cxc n1 intfrac sinn2 cxdxcos cx qquadmbox for nneq 1mbox intfrac sinn cxdxcosm cx frac sinn1 cxc m1cosm1 cxfrac nm2m1intfrac sinn cxdxcosm2 cx qquadmbox for mneq 1mbox also intfrac sinn cxdxcosm cx frac sinn1 cxc nmcosm1 cxfrac n1nmintfrac sinn2 cxdxcosm cx qquadmbox for mneq nmbox also intfrac sinn cxdxcosm cx frac sinn1 cxc m1cosm1 cxfrac n1m1intfrac sinn2 cxdxcosm2 cx qquadmbox for mneq 1mbox intfrac cos cxdxsinn cx frac 1c n1sinn1 cx qquadmbox for nneq 1mbox intfrac cos2 cxdxsin cx frac 1cleft cos cxlnlefttanfrac cx2rightright intfrac cos2 cxdxsinn cx frac 1n1left frac cos cxcsinn1 cxintfrac dxsinn2 cxright qquadmbox for nneq 1mbox intfrac cosn cxdxsinm cx frac cosn1 cxc m1sinm1 cx frac nm2m1intfrac cosn cxdxsinm2 cx qquadmbox for mneq 1mbox also intfrac cosn cxdxsinm cx frac cosn1 cxc nmsinm1 cx frac n1nmintfrac cosn2 cxdxsinm cx qquadmbox for mneq nmbox also intfrac cosn cxdxsinm cx frac cosn1 cxc m1sinm1 cx frac n1m1intfrac cosn2 cxdxsinm2 cx qquadmbox for mneq 1mbox 積分只有 sin 和 tan 的函式 int sin cx tan cxdx frac 1clnsec cx tan cx sin cx intfrac tann cxdxsin2 cx frac 1c n1tann1 cx qquadmbox for nneq 1mbox 積分只有 cos 和 tan 的函式 intfrac tann cxdxcos2 cx frac 1c n1tann1 cx qquadmbox for nneq 1mbox 積分只有 sin 和 cot 的函式 intfrac cotn cxdxsin2 cx frac 1c n1cotn1 cx qquadmbox for nneq 1mbox 積分只有 cos 和 cot 的函式 intfrac cotn cxdxcos2 cx frac 1c 1ntan1n cx qquadmbox for nneq 1mbox 積分只有 tan 和 cot 的函式 int frac tanm cxcotn cxdx frac 1c mn1tanmn1cx int frac tanm2cxcotn cxdxqquadmbox for m n neq 1mbox Category 積分表 Category 三角學