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Going further with integration by parts. Don't know whether to proceed further or not

  1. Jan 28, 2013 #1
    Hey guys,

    Need you push to proceed further with integration by parts:

    ∫e3x*3*x2*ydx=y∫e3x*3*x2dx

    setting u=3*x2-------du=6*x dx
    dv= e3*xdx--- v= 1/3* e3*x

    ∫ e3*x*3*x2*ydx=y*(3*x2* 1/3* e3*x-∫6*x*1/3* e3*xdx)
    =y*(3*x2* 1/3* e3*x-6/3*∫x*e3*xdx)
    Solving further about x*e3*x
    u=x---du=dx
    dv=e3*xdx---v=1/3*e3*x
    ∫ e3*x*3*x2*ydx=y*(3*x2* 1/3* e3*x-6/3*(x*1/3*e3*x-∫1/3e3*x)
     
  2. jcsd
  3. Jan 28, 2013 #2
    Re: Going further with integration by parts. Don't know whether to proceed further or

    How can we go further with solution as exp(3*x) repeats all the time?
     
  4. Jan 28, 2013 #3

    Mark44

    Staff: Mentor

    Re: Going further with integration by parts. Don't know whether to proceed further or

    You've done all the hard work. ∫e3xdx is easy, using a simple substitution.
     
  5. Jan 29, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Going further with integration by parts. Don't know whether to proceed further or

    If you have [itex]\int x^n f(x)dx[/itex], where "f" is easy to integrate any number of times (and the "nth" integral of [itex]e^{3x}[/itex] is [itex](1/3^n)e^{3x}[/itex]), just continue taking [itex]u= x^n[/itex], [itex]dv= f(x)dx[/itex]. Everytime du will have x to a lower power until, eventually, it is just [itex]x^0= 1[/itex].
     
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