Integrales Resueltas

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INTEGRACION POR PARTES
Cristhian Antonio Maldonado Pavón
6° Sem. “BMIN”Informática |

* ∫In x dx=
u=In x dv=dx
du=dxx v=x
In x dx=x In x- xdxx
In x dx= x In x-dx
In x dx= x In x-x+C
In x dx=x In x-1+C

* x2exdx=
u=x2 dv=exdxdu=2x dx v= ex
x2exdx=x2 ex-2x ex dx
x2exdx=x2 ex-2x ex dx
u=x dv= exdx
du=dx v=ex
x2exdx=x2 ex-2( x ex- ex dx)
x2exdx=x2 ex-2 x ex- 2 ex+C
x2exdx=ex(x2-2 x - 2 )+C

* x cos2x dx=
u=x dv=cos2x dx
du=dx v= cosx sen x2+12cosx dx
x cos2x dx=x(cosx sen x2+12)-12 x+senx+cosxdx
x cos2x dx=x22+ xcosx sen x2-12(xdx sen xcosx dx)
x cos2xdx=x22+ xcosx sen x2-x44-1212 sen2x dx
x cos2x dx=x22+ xcosx sen x2-14sen 2x dx
x cos2x dx=x24+ xcosx sen x4-cos2x8+C

* x3sen x dx=
u=x3 dv=sen x dx
du=3x2 v= -cosx
x3sen x dx=-x3cosx--3 x2cosx dx
x3sen x dx=-x3cosx+3x2cosx dx
u=x2 dv=cos x dx
du=2x v= sen x
x3sen x dx=-x3cosx+3(x2 sen x-2 x sen x dx)
x3sen x dx=-x3cosx+3(x2 sen x-2x...