- #1
ƒ(x)
- 328
- 0
Please forgive any formatting errors.
[tex]\int x[/tex]exdx = ?
Is this correct?
[tex]\int x[/tex]exdx
= [tex]\int e[/tex]ln(x)exdx
= [tex]\int e[/tex]exln(x)dx
u = ex
x = ln(u)
du = exdx
[tex]du/u[/tex] = dx
= ∫ ln(u)u*(1/u)*du
a = ln(u)u
EDIT: da = ln(u)u-1du
dv = 1/u du
v = ln(u)
= ln(u)u+1 - ∫ [ln(u)]udu
u = ex
= ln(ex)ex+1 - ∫ [ln(ex)]exdx
∫xexdx = xex+1-∫xexdx
2∫xexdx = xex+1
∫xexdx = xex+1*(1/2)+C
[tex]\int x[/tex]exdx = ?
Is this correct?
[tex]\int x[/tex]exdx
= [tex]\int e[/tex]ln(x)exdx
= [tex]\int e[/tex]exln(x)dx
u = ex
x = ln(u)
du = exdx
[tex]du/u[/tex] = dx
= ∫ ln(u)u*(1/u)*du
a = ln(u)u
EDIT: da = ln(u)u-1du
dv = 1/u du
v = ln(u)
= ln(u)u+1 - ∫ [ln(u)]udu
u = ex
= ln(ex)ex+1 - ∫ [ln(ex)]exdx
∫xexdx = xex+1-∫xexdx
2∫xexdx = xex+1
∫xexdx = xex+1*(1/2)+C
Last edited: