Formulario general de calculo
- 1. FORMULARIO GENERAL DE CLCULO Derivadas: d d c=0 x =1 dx dx d du d du dv cu = c ( u + v + ...) = + + ... dx dx dx dx dx d n d n du x = nx n1 u = nu n 1 dx dx dx du dv v u d dv du d 錚 u 錚 dx dx uv = u +v 錚 錚= dx dx dx dx 錚 v 錚 v 2 du d d u du u = dx a = au l n a dx 2 u dx dx d du d du senu = cosu cosu = s e n u dx dx dx dx d du d du tanu = sec2 u cotu = csc2 u dx dx dx dx d du d du secu = tanusecu cscu = cotucscu dx dx dx dx du d d u du lnu = dx e = eu dx u dx dx 1
- 2. du du d dx d dx arc senu = arccosu = dx 1 u2 dx 1 u2 du du d d arctanu = dx 2 arccotu = dx 2 dx 1+ u dx 1+ u du du d dx d dx arc secu = arccscu = dx u u2 1 dx u u2 1 Integrales: dx = x + c cudx = c udx x n+1 x dx = +c para n 1 n n+1 dx x = ln x + c ( u + v + ...) dx = u d x + v d x + ... u n +1 u du = +c para u 1 n n +1 du = lnu + c e du = e +c u u u u + a dx = 2 2 u 2 u +a + 2 a2 2 ln u + 2 ( u 2 + a2 )+ c u a du = 2 2 u 2 u a 2 a2 2 2 ln u + ( u2 a2 )+ c 2
- 3. u a2 u a u du = a u + arc sen + c 2 2 2 2 2 2 a u +a du 2 2 ( = ln u + ) u 2 + a2 + c u a du 2 2 ( = ln u + u 2 a2 )+ c du u a2 u2 = arc sen a +c du 1 u u +a 2 2 = a arctan a +c du 1 ua u a 2 2 = 2a ln u+a +c du 1 a+u a u 2 2 = 2a ln au +c sen u d u = cosu + c cosudu = sen u + c tanudu = ln secu + c cotudu = ln senu + c secu du = ln (tanu + secu ) + c cscudu = ln ( cscu cotu ) + c sec u d u = tanu + c csc u du = cotu + c 2 2 tanusecu du = tanu + c cotucscudu = cscu + c principales identidades utilizadas en las integrales trigonom辿tricas: sen2 x + cos 2 x = 1 tan 2 x + 1 = sec2 x 1 cot 2 x + 1 = csc 2 x sen2 x = (1 cos 2x ) 2 3
- 4. 1 cos 2 x = (1 + cos 2 x ) sen 2 x = 2 sen x cosx 2 sen x cosx tanx = cot x = cosx sen x 1 1 secx = cscx = cos x sen x integraci坦n por partes: udv = uv vdu cambios de variable trigonom辿tricos: para el radical hacer el cambio b a 2x 2 + b 2 x= tan t a b a2 x 2 b2 x= sect a b b 2 a 2 x2 x= sent a 4