Tabla de integrales

Tabla de integrales
expresión | Integral | expresión | Integral |
du | U+c | adu | a.u+c |
ardu | ur+1r+1 :r≠-1 | duy | lnu+c |
audu | auln(a)+c | eudu | eu+c|
sin(u)du | -cos(u)+c | cos(u)du | Sen(u)+c |
tan(u)du | lnsecu+c | cot(u)du | lnsenu+c |
sec(u)du | lnsecu+tgu+c | csc(u)du | -ln[cscu+ctg(u)]+c |
sec2(u)du |Tg(u)+c | csc2(u)du | -ctg(u)+c |
secu.tg(u)du | Sec(u)+c | cscu.ctg(u)du | -csc(u)+c |
1a2-u2du | arcosenua+c :a>0 | -1a2-u2du | arccos(ua)+c a>0 |1a2+u2du | 1aarctgua+c | -1a2+u2du | 1aarctgua+c |
1u.a2-u2du | 1aarcsecua+c | -1u.a2-u2du | 1aarccscua+c |

Identidades trigonométricas
tanx= sinxcosx | sen2x+cos2x=1|
cotx=1tanx= cosxsinx | tg2x+1=sec2(x) |
secx= 1cosx | ctg2x+1=csc2(x) |
cosx= 1secx | Sen(x+y)=sen(x).cos(x)+cos(x).sen(y) |
cscx= 1sinx |Sen(x-y)=sen(x).cos(y)-cos(x).sen(y) |
sinx= 1cscx | Cos(x+y)=cos(x).cos(y)-sen(x).sen(y) |
Sen(2x)=2sen(x).cos(x) | Cos(2x)cos2x-sen2(x) |
sen2x=1-cos⁡(2x)2 | cos2x=1+cos⁡(2x)2 |Tg(x+y)=tgx+tg(y)1-tgx.tg(y) | Tg(x-y)= tgx-tg(y)1+tgx.tg(y) |
Tg(2x)=2tg(x)1-tg2(x) |

Tabla de derivadas
función | derivada | función | derivada |
Y= c | Y’= 0| Y = x | Y´= 1 |
Y=c.u | Y´=c.u´ | Y=yr | Y´=r.ur-1.u´ |
Y=u.v | Y´=u´.v+u.v´ | y=uv | Y´=u´.v-u.v´v2 |
Y=sen(u) | Y´=cos(U).u´ | Y=cos(u) | Y´=-sen(u).u´ |Y=tg(u) | Y´=sec(u).tg(U).u´ | Y=ctg(u) | Y´=csc2u.u´ |
Y=sec(u) | Y´=sec(u).tg(u).u´ | Y=csc(u) | Y´=-csc(u).ctg(u).u´ |
Y=arcsen(u) | Y´=11-u2.u´ | Y=arccos(u) |Y´=-11-u2.u´ |
Y=arcsec(u) | Y´=1IuI.1-u2.u´ | Y=arccsc(u) | Y´=-1IuI1-u2.u´ |
Y=au | Y´=au.lna.u´ | Y=eu | Y´=eu.u´ |
Y=loga(u) | Y´=u´u.ln⁡(a) | Y=ln(u) | Y´=u´u |