Problemas de calculo integral

1………………………….. xe-3xdx

µ=x dv=e-3xdx
dµ=dx v=dv=e-3x dx=-13e-3x+c
v=-e-3x3
x-e-3x3-[-e-3x3]dx
-xe-3x3+13e-3x-3dx
I=-xe-3x3-19e-3x+c
I=-xe-3x3-e-3x9+cI=-9(xe-3x)-3(e-3x)27+c

2………..26x2 ex dx

µ=26x2 dv=ex dx
dµ=52x dx v=dv=exdx=ex+c
µ dv=µv-ex-v dx
26x2e2-ex52x dx
26x2ex-152exx dx=26x2ex-152ex=26x2ex-ex52
I=1352x2ex-ex52

3…………..03x2ex3dxdv=03x2 µ=ex3
v=dv=03=x2=03x33 dµ=ex3 3x3dx
v=x3
I=ex3x3-x3ex33x2dx
I=x3ex3-x3ex33x2dx
µ=x3 dv2=ex33x2 dx
dµ=3x2dx v=dv=ex33x2dx
v= ex3
I11=x3ex3-x3ex3-ex33x2dxI11=ex3-x3ex3-ex3
I11= -ex3
4………tln(0t+06)dt
dlnVdx= lv.dvdx
I=tln0t t06dt µ= ln⁡(0t+06)
dµ=1(ot+06)dt
dv=tdt
v=dv dt=tdt
v=t22
I=ln0t+06t22-12t2[10t+06]dt
I=t2ln⁡(0t+06)2-120t+06t33+c=t2ln⁡(0t+06)2-0t+06t312+c
I=6t2ln0t+06-2t3(0t+06)24

5 …………………...(lnx)206xdx
dx=(lnx)6ln06xdx
µ=lnx dv=ln06xdx
dµ=(lnx)5 1xdx v=dv=ln06xdxµdv=µv-vdµ v=06xln06x-06x+c
I=lnx06xln06x-06x-06xln06x-06x

6……………….xe2x2x+062dx
xe2x(2x+06)2dx
µ=(2x+06)-2=1(2x+06)2 dv=xe2xdx
dµ=-2(2x+06)-12txv=dv=xe2xdx
dµ=-4(2x+06)dx v=xe2xdxµ=xdv=e2xdx
dµ=xdx v=v=
=1(2x+06)2e2x2-12e2x-42x+06dx v=e2x2dxv=12e2x

I=e2X2(2x+06)2+12[42x+06] e2x+cv=e2x2

I=e2x2(2x+06)2+e2x82x+06=e2x2(2x+06)2+e2x(2x+06)8

I=8e2X(2x2+06)2+2e2x(2x2-06)316(2x+06)2

7………………..(x2-6)exdx
µ=x2-6 dv=exdx
dµ=2x v v=dv=exdx...