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La siguiente es una lista de integrales de funciones trigonométricas y su correspondiente simplificación. La letra c representa una constante numérica.

Integrales que contienen solamente sin

∫sin⁡cxdx=−1ccos⁡cx{displaystyle int sin cx;dx=-{frac {1}{c}}cos cx}

∫sinn⁡cxdx=−sinn−1⁡cxcos⁡cxnc+n−1n∫sinn−2⁡cxdx(para n>0){displaystyle int sin ^{n}cx;dx=-{frac {sin ^{n-1}cxcos cx}{nc}}+{frac {n-1}{n}}int sin ^{n-2}cx;dxqquad {mbox{(para }}n>0{mbox{)}}}

∫xsin⁡cxdx=sin⁡cxc2−xcos⁡cxc{displaystyle int xsin cx;dx={frac {sin cx}{c^{2}}}-{frac {xcos cx}{c}}}

∫xnsin⁡cxdx=−xnccos⁡cx+nc∫xn−1cos⁡cxdx(para n>0){displaystyle int x^{n}sin cx;dx=-{frac {x^{n}}{c}}cos cx+{frac {n}{c}}int x^{n-1}cos cx;dxqquad {mbox{(para }}n>0{mbox{)}}}

∫sin⁡cxxdx=∑i=0∞(−1)i(cx)2i+1(2i+1)⋅(2i+1)!{displaystyle int {frac {sin cx}{x}}dx=sum _{i=0}^{infty }(-1)^{i}{frac {(cx)^{2i+1}}{(2i+1)cdot (2i+1)!}}}

∫sin⁡cxxndx=−sin⁡cx(n−1)xn−1+cn−1∫cos⁡cxxn−1dx{displaystyle int {frac {sin cx}{x^{n}}}dx=-{frac {sin cx}{(n-1)x^{n-1}}}+{frac {c}{n-1}}int {frac {cos cx}{x^{n-1}}}dx}

∫dxsin⁡cx=1cln⁡|tan⁡cx2|{displaystyle int {frac {dx}{sin cx}}={frac {1}{c}}ln left|tan {frac {cx}{2}}right|}

∫dxsinn⁡cx=cos⁡cxc(1−n)sinn−1⁡cx+n−2n−1∫dxsinn−2⁡cx(para n>1){displaystyle int {frac {dx}{sin ^{n}cx}}={frac {cos cx}{c(1-n)sin ^{n-1}cx}}+{frac {n-2}{n-1}}int {frac {dx}{sin ^{n-2}cx}}qquad {mbox{(para }}n>1{mbox{)}}}

∫dx1±sin⁡cx=1ctan⁡(cx2∓π4){displaystyle int {frac {dx}{1pm sin cx}}={frac {1}{c}}tan left({frac {cx}{2}}mp {frac {pi }{4}}right)}

∫xdx1−sin⁡cx=xccot⁡(π4−cx2)+2c2ln⁡|sin⁡(π4−cx2)|{displaystyle int {frac {x;dx}{1-sin cx}}={frac {x}{c}}cot left({frac {pi }{4}}-{frac {cx}{2}}right)+{frac {2}{c^{2}}}ln left|sin left({frac {pi }{4}}-{frac {cx}{2}}right)right|}

∫sin⁡cxdx1±sin⁡cx=±x+1ctan⁡(π4∓cx2){displaystyle int {frac {sin cx;dx}{1pm sin cx}}=pm x+{frac {1}{c}}tan left({frac {pi }{4}}mp {frac {cx}{2}}right)}

∫sin⁡c1xsin⁡c2xdx=sin⁡(c1−c2)x2(c1−c2)−sin⁡(c1+c2)x2(c1+c2)(para |c1|≠|c2|){displaystyle int sin c_{1}xsin c_{2}x;dx={frac {sin(c_{1}-c_{2})x}{2(c_{1}-c_{2})}}-{frac {sin(c_{1}+c_{2})x}{2(c_{1}+c_{2})}}qquad {mbox{(para }}|c_{1}|neq |c_{2}|{mbox{)}}}

Integrales que contienen solamente cos

∫cos⁡cxdx=1csin⁡cx{displaystyle int cos cx;dx={frac {1}{c}}sin cx}

∫cosn⁡cxdx=cosn−1⁡cxsin⁡cxnc+n−1n∫cosn−2⁡cxdx(para n>0){displaystyle int cos ^{n}cx;dx={frac {cos ^{n-1}cxsin cx}{nc}}+{frac {n-1}{n}}int cos ^{n-2}cx;dxqquad {mbox{(para }}n>0{mbox{)}}}

∫xcos⁡cxdx=cos⁡cxc2+xsin⁡cxc{displaystyle int xcos cx;dx={frac {cos cx}{c^{2}}}+{frac {xsin cx}{c}}}

∫xncos⁡cxdx=xnsin⁡cxc−nc∫xn−1sin⁡cxdx{displaystyle int x^{n}cos cx;dx={frac {x^{n}sin cx}{c}}-{frac {n}{c}}int x^{n-1}sin cx;dx}

∫cos⁡cxxdx=ln⁡|cx|+∑i=1∞(−1)i(cx)2i2i⋅(2i)!{displaystyle int {frac {cos cx}{x}}dx=ln |cx|+sum _{i=1}^{infty }(-1)^{i}{frac {(cx)^{2i}}{2icdot (2i)!}}}

∫cos⁡cxxndx=−cos⁡cx(n−1)xn−1−cn−1∫sin⁡cxxn−1dx(para n≠1){displaystyle int {frac {cos cx}{x^{n}}}dx=-{frac {cos cx}{(n-1)x^{n-1}}}-{frac {c}{n-1}}int {frac {sin cx}{x^{n-1}}}dxqquad {mbox{(para }}nneq 1{mbox{)}}}

∫dxcos⁡cx=1cln⁡|tan⁡(cx2+π4)|{displaystyle int {frac {dx}{cos cx}}={frac {1}{c}}ln left|tan left({frac {cx}{2}}+{frac {pi }{4}}right)right|}

∫dxcosn⁡cx=sin⁡cxc(n−1)cosn−1cx+n−2n−1∫dxcosn−2⁡cx(para n>1){displaystyle int {frac {dx}{cos ^{n}cx}}={frac {sin cx}{c(n-1)cos^{n-1}cx}}+{frac {n-2}{n-1}}int {frac {dx}{cos ^{n-2}cx}}qquad {mbox{(para }}n>1{mbox{)}}}

∫dx1+cos⁡cx=1ctan⁡cx2{displaystyle int {frac {dx}{1+cos cx}}={frac {1}{c}}tan {frac {cx}{2}}}

∫dx1−cos⁡cx=−1ccot⁡cx2{displaystyle int {frac {dx}{1-cos cx}}=-{frac {1}{c}}cot {frac {cx}{2}}}

∫xdx1+cos⁡cx=xctan⁡cx2+2c2ln⁡|cos⁡cx2|{displaystyle int {frac {x;dx}{1+cos cx}}={frac {x}{c}}tan {cx}{2}+{frac {2}{c^{2}}}ln left|cos {frac {cx}{2}}right|}

∫xdx1−cos⁡cx=−xxcot⁡cx2+2c2ln⁡|sin⁡cx2|{displaystyle int {frac {x;dx}{1-cos cx}}=-{frac {x}{x}}cot {cx}{2}+{frac {2}{c^{2}}}ln left|sin {frac {cx}{2}}right|}

∫cos⁡cxdx1+cos⁡cx=x−1ctan⁡cx2{displaystyle int {frac {cos cx;dx}{1+cos cx}}=x-{frac {1}{c}}tan {frac {cx}{2}}}

∫cos⁡cxdx1−cos⁡cx=−x−1ccot⁡cx2{displaystyle int {frac {cos cx;dx}{1-cos cx}}=-x-{frac {1}{c}}cot {frac {cx}{2}}}

∫cos⁡c1xcos⁡c2xdx=sin⁡(c1−c2)x2(c1−c2)+sin⁡(c1+c2)x2(c1+c2)(para |c1|≠|c2|){displaystyle int cos c_{1}xcos c_{2}x;dx={frac {sin(c_{1}-c_{2})x}{2(c_{1}-c_{2})}}+{frac {sin(c_{1}+c_{2})x}{2(c_{1}+c_{2})}}qquad {mbox{(para }}|c_{1}|neq |c_{2}|{mbox{)}}}

Integrales que contienen solamente tan

∫tan⁡cxdx=−1cln⁡|cos⁡cx|{displaystyle int tan cx;dx=-{frac {1}{c}}ln |cos cx|}

∫tann⁡cxdx=1c(n−1)tann−1⁡cx−∫tann−2⁡cxdx(para n≠1){displaystyle int tan ^{n}cx;dx={frac {1}{c(n-1)}}tan ^{n-1}cx-int tan ^{n-2}cx;dxqquad {mbox{(para }}nneq 1{mbox{)}}}

∫dxtan⁡cx+1=x2+12cln⁡|sin⁡cx+cos⁡cx|{displaystyle int {frac {dx}{tan cx+1}}={frac {x}{2}}+{frac {1}{2c}}ln |sin cx+cos cx|}

∫dxtan⁡cx−1=−x2+12cln⁡|sin⁡cx−cos⁡cx|{displaystyle int {frac {dx}{tan cx-1}}=-{frac {x}{2}}+{frac {1}{2c}}ln |sin cx-cos cx|}

∫tan⁡cxdxtan⁡cx+1=x2−12cln⁡|sin⁡cx+cos⁡cx|{displaystyle int {frac {tan cx;dx}{tan cx+1}}={frac {x}{2}}-{frac {1}{2c}}ln |sin cx+cos cx|}

∫tan⁡cxdxtan⁡cx−1=x2+12cln⁡|sin⁡cx−cos⁡cx|{displaystyle int {frac {tan cx;dx}{tan cx-1}}={frac {x}{2}}+{frac {1}{2c}}ln |sin cx-cos cx|}

Integrales que contienen solamente cot

∫cot⁡cxdx=1cln⁡|sin⁡cx|{displaystyle int cot cx;dx={frac {1}{c}}ln |sin cx|}

∫cotn⁡cxdx=−1c(n−1)cotn−1⁡cx−∫cotn−2⁡cxdx(para )n≠1){displaystyle int cot ^{n}cx;dx=-{frac {1}{c(n-1)}}cot ^{n-1}cx-int cot ^{n-2}cx;dxqquad {mbox{(para )}}nneq 1{mbox{)}}}

∫dx1+cot⁡cx=∫tan⁡cxdxtan⁡cx+1{displaystyle int {frac {dx}{1+cot cx}}=int {frac {tan cx;dx}{tan cx+1}}}

∫dx1−cot⁡cx=∫tan⁡cxdxtan⁡cx−1{displaystyle int {frac {dx}{1-cot cx}}=int {frac {tan cx;dx}{tan cx-1}}}

Integrales que contienen sen y cos

∫dxcos⁡cx±sin⁡cx=1c2ln⁡|tan⁡(cx2±π8)|{displaystyle int {frac {dx}{cos cxpm sin cx}}={frac {1}{c{sqrt {2}}}}ln left|tan left({frac {cx}{2}}pm {frac {pi }{8}}right)right|}

∫dx(cos⁡cx±sin⁡cx)2=12ctan⁡(cx∓π4){displaystyle int {frac {dx}{(cos cxpm sin cx)^{2}}}={frac {1}{2c}}tan left(cxmp {frac {pi }{4}}right)}

∫cos⁡cxdxcos⁡cx+sin⁡cx=x2+12cln⁡|sin⁡cx+cos⁡cx|{displaystyle int {frac {cos cx;dx}{cos cx+sin cx}}={frac {x}{2}}+{frac {1}{2c}}ln left|sin cx+cos cxright|}

∫cos⁡cxdxcos⁡cx−sin⁡cx=x2−12cln⁡|sin⁡cx−cos⁡cx|{displaystyle int {frac {cos cx;dx}{cos cx-sin cx}}={frac {x}{2}}-{frac {1}{2c}}ln left|sin cx-cos cxright|}

∫sin⁡cxdxcos⁡cx+sin⁡cx=x2−12cln⁡|sin⁡cx+cos⁡cx|{displaystyle int {frac {sin cx;dx}{cos cx+sin cx}}={frac {x}{2}}-{frac {1}{2c}}ln left|sin cx+cos cxright|}

∫sin⁡cxdxcos⁡cx−sin⁡cx=−x2−12cln⁡|sin⁡cx−cos⁡cx|{displaystyle int {frac {sin cx;dx}{cos cx-sin cx}}=-{frac {x}{2}}-{frac {1}{2c}}ln left|sin cx-cos cxright|}

∫cos⁡cxdxsin⁡cx(1+cos⁡cx)=−14ctan2⁡cx2+12cln⁡|tan⁡cx2|{displaystyle int {frac {cos cx;dx}{sin cx(1+cos cx)}}=-{frac {1}{4c}}tan ^{2}{frac {cx}{2}}+{frac {1}{2c}}ln left|tan {frac {cx}{2}}right|}

∫cos⁡cxdxsin⁡cx(1+−cos⁡cx)=−14ccot2⁡cx2−12cln⁡|tan⁡cx2|{displaystyle int {frac {cos cx;dx}{sin cx(1+-cos cx)}}=-{frac {1}{4c}}cot ^{2}{frac {cx}{2}}-{frac {1}{2c}}ln left|tan {frac {cx}{2}}right|}

∫sin⁡cxdxcos⁡cx(1+sin⁡cx)=14ccot2⁡(cx2+π4)+12cln⁡|tan⁡(cx2+π4)|{displaystyle int {frac {sin cx;dx}{cos cx(1+sin cx)}}={frac {1}{4c}}cot ^{2}left({frac {cx}{2}}+{frac {pi }{4}}right)+{frac {1}{2c}}ln left|tan left({frac {cx}{2}}+{frac {pi }{4}}right)right|}

∫sin⁡cxdxcos⁡cx(1−sin⁡cx)=14ctan2⁡(cx2+π4)−12cln⁡|tan⁡(cx2+π4)|{displaystyle int {frac {sin cx;dx}{cos cx(1-sin cx)}}={frac {1}{4c}}tan ^{2}left({frac {cx}{2}}+{frac {pi }{4}}right)-{frac {1}{2c}}ln left|tan left({frac {cx}{2}}+{frac {pi }{4}}right)right|}

∫sin⁡cxcos⁡cxdx=12csin2⁡cx{displaystyle int sin cxcos cx;dx={frac {1}{2c}}sin ^{2}cx}

∫sin⁡c1xcos⁡c2xdx=−cos⁡(c1+c2)x2(c1+c2)−cos⁡(c1−c2)x2(c1−c2)(para |c1|≠|c2|){displaystyle int sin c_{1}xcos c_{2}x;dx=-{frac {cos(c_{1}+c_{2})x}{2(c_{1}+c_{2})}}-{frac {cos(c_{1}-c_{2})x}{2(c_{1}-c_{2})}}qquad {mbox{(para }}|c_{1}|neq |c_{2}|{mbox{)}}}

∫sinn⁡cxcos⁡cxdx=1c(n+1)sinn+1⁡cx(para n≠1){displaystyle int sin ^{n}cxcos cx;dx={frac {1}{c(n+1)}}sin ^{n+1}cxqquad {mbox{(para }}nneq 1{mbox{)}}}

∫sin⁡cxcosn⁡cxdx=−1c(n+1)cosn+1⁡cx(para n≠1){displaystyle int sin cxcos ^{n}cx;dx=-{frac {1}{c(n+1)}}cos ^{n+1}cxqquad {mbox{(para }}nneq 1{mbox{)}}}

∫sinn⁡cxcosm⁡cxdx=−sinn−1⁡cxcosm+1⁡cxc(n+m)+n−1n+m∫sinn−2⁡cxcosm⁡cxdx(para m,n>0){displaystyle int sin ^{n}cxcos ^{m}cx;dx=-{frac {sin ^{n-1}cxcos ^{m+1}cx}{c(n+m)}}+{frac {n-1}{n+m}}int sin ^{n-2}cxcos ^{m}cx;dxqquad {mbox{(para }}m,n>0{mbox{)}}}

también: ∫sinn⁡cxcosm⁡cxdx=sinn+1⁡cxcosm−1⁡cxc(n+m)+m−1n+m∫sinn⁡cxcosm−2⁡cxdx(para m,n>0){displaystyle int sin ^{n}cxcos ^{m}cx;dx={frac {sin ^{n+1}cxcos ^{m-1}cx}{c(n+m)}}+{frac {m-1}{n+m}}int sin ^{n}cxcos ^{m-2}cx;dxqquad {mbox{(para }}m,n>0{mbox{)}}}

∫dxsin⁡cxcos⁡cx=1cln⁡|tan⁡cx|{displaystyle int {frac {dx}{sin cxcos cx}}={frac {1}{c}}ln left|tan cxright|}

∫dxsin⁡cxcosn⁡cx=1c(n−1)cosn−1⁡cx+∫dxsin⁡cxcosn−2⁡cx(para n≠1){displaystyle int {frac {dx}{sin cxcos ^{n}cx}}={frac {1}{c(n-1)cos ^{n-1}cx}}+int {frac {dx}{sin cxcos ^{n-2}cx}}qquad {mbox{(para }}nneq 1{mbox{)}}}

∫dxsinn⁡cxcos⁡cx=−1c(n−1)sinn−1⁡cx+∫dxsinn−2⁡cxcos⁡cx(para n≠1){displaystyle int {frac {dx}{sin ^{n}cxcos cx}}=-{frac {1}{c(n-1)sin ^{n-1}cx}}+int {frac {dx}{sin ^{n-2}cxcos cx}}qquad {mbox{(para }}nneq 1{mbox{)}}}

∫sin⁡cxdxcosn⁡cx=1c(n−1)cosn−1⁡cx(para n≠1){displaystyle int {frac {sin cx;dx}{cos ^{n}cx}}={frac {1}{c(n-1)cos ^{n-1}cx}}qquad {mbox{(para }}nneq 1{mbox{)}}}

∫sin2⁡cxdxcos⁡cx=−1csin⁡cx+1cln⁡|tan⁡(π4+cx2)|{displaystyle int {frac {sin ^{2}cx;dx}{cos cx}}=-{frac {1}{c}}sin cx+{frac {1}{c}}ln left|tan left({frac {pi }{4}}+{frac {cx}{2}}right)right|}

∫sin2⁡cxdxcosn⁡cx=sin⁡cxc(n−1)cosn−1⁡cx−1n−1∫dxcosn−2⁡cx(para n≠1){displaystyle int {frac {sin ^{2}cx;dx}{cos ^{n}cx}}={frac {sin cx}{c(n-1)cos ^{n-1}cx}}-{frac {1}{n-1}}int {frac {dx}{cos ^{n-2}cx}}qquad {mbox{(para }}nneq 1{mbox{)}}}

∫sinn⁡cxdxcos⁡cx=−sinn−1⁡cxc(n−1)+∫sinn−2⁡cxdxcos⁡cx(for n≠1){displaystyle int {frac {sin ^{n}cx;dx}{cos cx}}=-{frac {sin ^{n-1}cx}{c(n-1)}}+int {frac {sin ^{n-2}cx;dx}{cos cx}}qquad {mbox{(for }}nneq 1{mbox{)}}}

∫sinncxdxcosm⁡cx=sinn+1⁡cxc(m−1)cosm−1⁡cx−n−m+2m−1∫sinn⁡cxdxcosm−2⁡cx(para m≠1){displaystyle int {frac {sin^{n}cx;dx}{cos ^{m}cx}}={frac {sin ^{n+1}cx}{c(m-1)cos ^{m-1}cx}}-{frac {n-m+2}{m-1}}int {frac {sin ^{n}cx;dx}{cos ^{m-2}cx}}qquad {mbox{(para }}mneq 1{mbox{)}}}

también: ∫sinncxdxcosm⁡cx=−sinn−1⁡cxc(n−m)cosm−1⁡cx+n−1n−m∫sinn−2⁡cxdxcosm⁡cx(para m≠n){displaystyle int {frac {sin^{n}cx;dx}{cos ^{m}cx}}=-{frac {sin ^{n-1}cx}{c(n-m)cos ^{m-1}cx}}+{frac {n-1}{n-m}}int {frac {sin ^{n-2}cx;dx}{cos ^{m}cx}}qquad {mbox{(para }}mneq n{mbox{)}}}

también: ∫sinncxdxcosm⁡cx=sinn−1⁡cxc(m−1)cosm−1⁡cx−n−1n−1∫sinn−1⁡cxdxcosm−2⁡cx(para m≠1){displaystyle int {frac {sin^{n}cx;dx}{cos ^{m}cx}}={frac {sin ^{n-1}cx}{c(m-1)cos ^{m-1}cx}}-{frac {n-1}{n-1}}int {frac {sin ^{n-1}cx;dx}{cos ^{m-2}cx}}qquad {mbox{(para }}mneq 1{mbox{)}}}

∫cos⁡cxdxsinn⁡cx=−1c(n−1)sinn−1⁡cx(para n≠1){displaystyle int {frac {cos cx;dx}{sin ^{n}cx}}=-{frac {1}{c(n-1)sin ^{n-1}cx}}qquad {mbox{(para }}nneq 1{mbox{)}}}

∫cos2⁡cxdxsin⁡cx=1c(cos⁡cx+ln⁡|tan⁡cx2|){displaystyle int {frac {cos ^{2}cx;dx}{sin cx}}={frac {1}{c}}left(cos cx+ln left|tan {frac {cx}{2}}right|right)}

∫cos2⁡cxdxsinn⁡cx=−1n−1(cos⁡cxcsinn−1⁡cx)+∫dxsinn−2⁡cx)(para n≠1){displaystyle int {frac {cos ^{2}cx;dx}{sin ^{n}cx}}=-{frac {1}{n-1}}left({frac {cos cx}{csin ^{n-1}cx)}}+int {frac {dx}{sin ^{n-2}cx}}right)qquad {mbox{(para }}nneq 1{mbox{)}}}

∫cosn⁡cxdxsinm⁡cx=−cosn+1⁡cxc(m−1)sinm−1⁡cx−n−m−2m−1∫cosncxdxsinm−2⁡cx(para m≠1){displaystyle int {frac {cos ^{n}cx;dx}{sin ^{m}cx}}=-{frac {cos ^{n+1}cx}{c(m-1)sin ^{m-1}cx}}-{frac {n-m-2}{m-1}}int {frac {cos^{n}cx;dx}{sin ^{m-2}cx}}qquad {mbox{(para }}mneq 1{mbox{)}}}

también: ∫cosn⁡cxdxsinm⁡cx=cosn−1⁡cxc(n−m)sinm−1⁡cx+n−1n−m∫cosn−2cxdxsinm⁡cx(para m≠n){displaystyle int {frac {cos ^{n}cx;dx}{sin ^{m}cx}}={frac {cos ^{n-1}cx}{c(n-m)sin ^{m-1}cx}}+{frac {n-1}{n-m}}int {frac {cos^{n-2}cx;dx}{sin ^{m}cx}}qquad {mbox{(para }}mneq n{mbox{)}}}

también: ∫cosn⁡cxdxsinm⁡cx=−cosn−1⁡cxc(m−1)sinm−1⁡cx−n−1m−1∫cosn−2cxdxsinm−2⁡cx(para m≠1){displaystyle int {frac {cos ^{n}cx;dx}{sin ^{m}cx}}=-{frac {cos ^{n-1}cx}{c(m-1)sin ^{m-1}cx}}-{frac {n-1}{m-1}}int {frac {cos^{n-2}cx;dx}{sin ^{m-2}cx}}qquad {mbox{(para }}mneq 1{mbox{)}}}

Integrales que contienen sen y tan

∫sin⁡cxtan⁡cxdx=1c(ln⁡|sec⁡cx+tan⁡cx|−sin⁡cx){displaystyle int sin cxtan cx;dx={frac {1}{c}}(ln |sec cx+tan cx|-sin cx),!}

∫tann⁡cxdxsin2⁡cx=1fffc(n−1)tann−1⁡(cx)(para n≠1){displaystyle int {frac {tan ^{n}cx;dx}{sin ^{2}cx}}={frac {1}{f}}ff{c(n-1)}tan ^{n-1}(cx)qquad {mbox{(para }}nneq 1{mbox{)}},!}

Integrales que contienen cos y tan

∫tann⁡cxdxcos2⁡cx=1c(n+1)tann+1⁡cx(para n≠1){displaystyle int {frac {tan ^{n}cx;dx}{cos ^{2}cx}}={frac {1}{c(n+1)}}tan ^{n+1}cxqquad {mbox{(para }}nneq 1{mbox{)}}}

Integrales que contienen sen y cot

∫cotn⁡cxdxsin2cx=1c(n+1)cotn+1⁡cx(para n≠1){displaystyle int {frac {cot ^{n}cx;dx}{sin^{2}cx}}={frac {1}{c(n+1)}}cot ^{n+1}cxqquad {mbox{(para }}nneq 1{mbox{)}}}

Integrales que contienen cos y cot

∫cotn⁡cxdxcos2⁡cx=1c(1−n)tan1−n⁡cx(para n≠1){displaystyle int {frac {cot ^{n}cx;dx}{cos ^{2}cx}}={frac {1}{c(1-n)}}tan ^{1-n}cxqquad {mbox{(para }}nneq 1{mbox{)}},!}

Integrales que contienen tan y cot

∫cot⁡cxtan⁡cxdx=x {displaystyle int cot cxtan cx;dx=x }

Integrales que contienen sec

∫sec2⁡xdx=tan⁡x+c{displaystyle int sec ^{2}x;dx=tan x+c}

∫sec⁡xdx=ln⁡|sec⁡x+tan⁡x|+c{displaystyle int sec x;dx=ln |sec x+tan x|+c}