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Centro de Estudios Tecnológicos Industriales y de Servicios # 20

Integrantes:
* Jorge Luis Velueta Cabrera.
* Daniel del Carmen Hernández Vázquez.
* Juan Luis Sarao Vázquez.
* Ángel Ricardo Sánchez Casanova.

Materia: Matemáticas

Semestres: 6to Grupo: AMAM

Profesor: Ing. Pascual Peralta

Especialidad: Mantenimiento Automotriz

Calculo Integral
u = (3x + 4)
du= (3) dx
u = (3x + 4)
du = (3) dx
Ejercicios: Resolver las siguientes Integrales.
* cos3 x+4 dx = cosu du = sinu+c
13 cos3x+4 3 dx= 13 sin3x+4+c
u = 3x
du = 3 dx
u = 3x
du = 3 dx

* sec2 3x dx= sec2 u du= tanu+c
13 sec2 3x 3dx= 13 tan3x+c
u2= x2 a2=9
u = x a = 3
du = dx
u2= x2 a2=9
u = x a = 3
du = dx

* dxx2+9= dxu2+ a2=ln/u+ u2+ a2/ + c
dxx2+9= ln/ x + x2-9 / + c

* u = 9x+3
du = 9 dx
u = 9x+3
du = 9 dx
e9x+3dx= eu du= eu+c
19 e9x+3 9dx= 19 e9x+3+c
u = x2 dv = cosx dx
du = 2x dx v = - sinx
u = x2 dv = cosx dx
du = 2x dx v = - sinx

* x2 cosx dx= u dv=uv- v du

x2 cosx dx= - x2sinx+ 2x cosx dx
x2 cosx dx= - x2sinx+ 2x cosx dx
Continuación delproblema…………
Continuación del problema…………
x2 cosx dx= - x2sinx+ 2 x cosx dx……Y
Integrando -.-‘
u = x dv = cosx dx
du = dx v = - sinx
u = x dv = cosx dx
du = dx v = - sinx
x cosx dx= - xsinx+ sinx dx
x cosx dx= - xsinx+cosx+c
Sustituyendo en (Y)
x2cosx dx=x2cosx -2-xsinx+cosx+c
x2cosx dx= x2cosx +2xsinx-2cosx+c

* u = xdv = exdx
du = dx v = ex
u = x dv = exdx
du = dx v = ex
xexdx u dv=uv-v du
xexdx=xex-exdx
xexdx=xex-ex+c
u = x dv = lnxdx
du = dx v = lnx
u = x dv = lnxdx
du = dx v = lnx

* xlnx dx u dv=uv-vdu
xlnx dx=xlnx-lnx dx
xlnx dx=xlnx-lnx+c

* sec2xtan2x dx secutanu du= secu+c
u= 2xdu= 2 dx
u= 2x
du= 2 dx
12sec2x tan2x2dx=12sec2x+c

* u= 5x
du= 5 dx
u= 5x
du= 5 dx
sin5x dx= secu du= -cosu+c
15sin5x5dx= -15 cos5x+c

* 5x4-3x5-6x2+4x-12dx=

5x55-3x44-6x33+4x22-12x+c

* u2=16
u= 4 a2=4x2
du= dx a= 2x
u2=16
u= 4 a2=4x2
du= dx a= 2x
dx16+4x2= duu2+a2=12aln/ u-au+a /+cdx16+4x2=12(2x) ln/4-2x4+2x /+c
u= 9x+4
du= 9 dx
u= 9x+4
du= 9 dx

* dx9x+4=duu=ln/u/+c

199dx9x+4 = 19ln/9x+4/+c
3
3

* 8x3-4 x2dx=umdu=um+1m+1+c
u= 8x3-4
du= 24x2dx
m = 3
u= 8x3-4
du= 24x2dx
m = 3
3
3
4
4
3
3

1248x3-4 24x2dx=1248x3-44 +c

u= x3
du= 3x2dx
dv = sinx dx
v = - cosx
u= x3
du= 3x2dx
dv = sinx dx
v = - cosx
3
3
4
41248x3-424x2dx=8x3-496 +c

* x3sinx dx=u dv=uv-v du
x3sinx dx=-x3cosx+3x2cosx dx
x3sinx dx=-x3cosx+3x2sinx dx …..(A)
U= x2 dv= cosx dx
du= 2x dx v= -sinx
U= x2 dv= cosx dx
du= 2x dx v= -sinx
Integrando
x2sinx dx=
x2sinx dx=-x2cosx+2xcosx dx
x2sinx dx=-x2cosx+2xcosx dx
Integrando
xcosx dx=
x cosx dx= -xsinx+sinx dx
x cosxdx=-xsinx+cosx+c
Sustituyendo en (A)
x3sinx dx=x3sinx-3-xsinx+cosx+c
x3sinx dx=x3sinx+3xsinx-3cosx+c

* U= x2 dv= exdx
du= 2x dx v= ex
U= x2 dv= exdx
du= 2x dx v= ex
x2exdx= u dv=uv-v du
x2exdx=x2ex-2xexdx
x2exdx=x2ex-2xexdx……(W)
Integrando
U = x dv =exdx
du = dx v = ex
U = x dv =exdx
du = dx v = ex
xexdx=xexdx=xex-exdx
xexdx=xex-ex+c
Sustituyendo en (W)
x2exdx=x2ex-2xee-ex+c
x2exdx=x2ex-2xex-2ex+c
x2exdx=exx2-2x-2+c

* U = x3 dv = lnx dx
du = 3x dx v = lnx
U = x3 dv = lnx dx
du = 3x dx v = lnx
x3lnx dx= u dv=uv-v du
x3lnx dx=x3lnx-3x2lnx dx
x3lnx dx=x3lnx-3x2lnx dx……(M)
Integrando
U = x2 dv = lnx dx
du = 2x dx v = lnx
U = x2...
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