Integrales

Pnf de Informatica Seccion 01
Realizado por:
Cabrera Arcelys
# 20.992.304

Ejercicios integrales por parte:
Ejercicio # 2
ʃ x e-xdx =
u=x dv=e-xdxdu=dx ʃ dv = ʃ e-xdx
v= - e-x
= x (- e-x) - ʃ-e-xdx
= x (- e-x) + ʃe-xdx
= x (-e-x) -e-x +C
= -e-x(x+1)+CSaco factor comun -e-x :

Ejercicio #3
ʃ x sen2 (3x) dx =
u=x dv= sen2 (3x) dx
du=dx ʃ dv = ʃ sen2 (3x) dxv= ʃ 12 ( 1 – cos (6x) ) dx = ʃ 12 - 12 cos (6x) ) dx

v=12 dx - 12 cos 6x dx
v= 12x- 12. 16 sen (6x)
v= 12x- 112 sen (6x)
ʃx sen2 (3x) dx = x 1 2 x- 1 12 sen (6x) - 1 2 x- 1 12 sen (6x) dx
= x1 2 x- 1 12 sen (6x) - 1 2 xdx + 1 12 sen 6xdx

= x1 2 x- 1 12 sen (6x) - 1 2 * x22 - 1 12* 1 6cos (6x) dx
= x12 x- 1 12 sen (6x) - 1 4 x2 - 1 72cos 6x+ C

Ejercicio # 4
ʃ x2 Lnx dx
u=Ln x du= dxx
dv= x2dx ʃ dv=ʃ x2dx v=x33
=lnx x33-13 ʃ x2 dx
=lnxx33-13 *x33+C
Saco factor comun x33
=x3 3 lnx-13+C

Ejercicio # 0
x3 ex3 dx
u=x3 du=3 x2 dx
dv= ex3 dx ʃ dv=ʃ ex3 dx v=3 ex3
ᵾ= x2 dᵾ=2xdxdᶌ= ex3 dx
ᶌ= 3 ex3

x3 3 ex3 3 ex3 3x2dx
= x3 3 ex3 -9 ex3 x2 dx


x3*ex3 dx= x3 3 ex3 -9 x2*3 ex3 - 3 ex3 2xdx
= x3*3 ex3 -9 x2* 3 ex3 -6 ex3 xdx
u= x du=dx
dv= ex3 dx ʃdv=ʃ ex3 dx
v= 3 ex3

=x3*3ex3 -27 x2ex3- 54 ex3 xdx

=x3*3ex3-27 x2ex3- 54 x 3ex3- 3ex3 dx
=x3*3ex3 -27 x2ex3- 54 x 3ex3-3*3 ex3 +C
=x3*3ex3 -27 x2ex3- 54 x 3 ex3-54*3*3 ex3+C
Saco factor comun 3 ex3
=3ex3 x3-9 x2-54 x-162 +C