integration by parts:
u=x, du=dx
dv=exp(-x/3) dx, v=-3exp(-x/3)
∫udv = uv-∫vdu
-3x*exp(-x/3) + 3∫exp(-x/3) dx
=-3x*exp(-x/3) - 9*exp(-x/3) + C
= -3*exp(-x/3)*(x+3) + C
you will have to use integration by parts,
let u = x and v'=e^(-x/3)
so u'= 1 and v= -3e^(-x/3)
so the integral will be equal to
fx= uv - int(vu') (uv= -3xe^(-x/3), and vu'= -3e^(-x/3)
so fx= -3xe^(-x/3) - intergral(-3e^(-x/3))
fx= -3xe^(-x/3) + 9e^(-x/3) + C
im sorry i had to write it in bad notation but im very limited with keyboard knowledge
i hope this helps
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Verified answer
integration by parts:
u=x, du=dx
dv=exp(-x/3) dx, v=-3exp(-x/3)
∫udv = uv-∫vdu
-3x*exp(-x/3) + 3∫exp(-x/3) dx
=-3x*exp(-x/3) - 9*exp(-x/3) + C
= -3*exp(-x/3)*(x+3) + C
you will have to use integration by parts,
let u = x and v'=e^(-x/3)
so u'= 1 and v= -3e^(-x/3)
so the integral will be equal to
fx= uv - int(vu') (uv= -3xe^(-x/3), and vu'= -3e^(-x/3)
so fx= -3xe^(-x/3) - intergral(-3e^(-x/3))
fx= -3xe^(-x/3) + 9e^(-x/3) + C
im sorry i had to write it in bad notation but im very limited with keyboard knowledge
i hope this helps