Integrating the product of an exponential and a first derivative

  • Thread starter bventer
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  • #1
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Hi, besides integration by parts, does anyone know of a simple integration trick to solve the integral (wrt x) of exp(x)*f'(x)?
 
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  • #2
Mentallic
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Could you show me how it's done by integration by parts?
 
  • #3
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Using integration by parts I get: exp(x)*f(x) - Int[exp(x)*f(x), dx]. But that doesn't really help me due to the complexity of the function f(x). I was hoping there might be a clever trick to exploit the fact that part of my integrand is a first derivative?
 
  • #4
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that doesn't really help me due to the complexity of the function f(x).
Why not showing us what is f '(x) ?
 
  • #5
Mentallic
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Using integration by parts I get: exp(x)*f(x) - Int[exp(x)*f(x), dx]. But that doesn't really help me due to the complexity of the function f(x). I was hoping there might be a clever trick to exploit the fact that part of my integrand is a first derivative?

Oh sorry, I missed the ' in f'(x) and thought you tried to find a solution to the integral of exf(x).

I can't think of another way to show it besides that technique, maybe someone else can.
 
  • #6
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To JJacquelin: I you wish, see attached jpg (apologies, but I am not well versed in Latex)
 

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  • #7
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Oh sorry, I missed the ' in f'(x) and thought you tried to find a solution to the integral of exf(x).

I can't think of another way to show it besides that technique, maybe someone else can.
Ok, thanks for having a look Mentallic
 
  • #8
Mentallic
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To JJacquelin: I you wish, see attached jpg (apologies, but I am not well versed in Latex)

How is the y(H) function defined?
 
  • #9
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How is the y(H) function defined?
y(H) is a quadratic: a0 + a1*H + a2*H^2
 
  • #10
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Probably, there is no analytic way to integrate a so complicated function.
Better think to use numerical calculus, or approximations if it is a problem of physics.
 
  • #11
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Thanks JJacquelin, but I did say that I was hoping there might be a clever trick to exploit the fact that part of my integrand is a first derivative...
 
  • #12
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I was hoping there might be a clever trick to exploit the fact that part of my integrand is a first derivative...
I doubt that a "clever trick" exists. By the way, the first derivative of what function ?
If the function is as complicated as its derivative,then there is few hope.
 
  • #13
HallsofIvy
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Thanks JJacquelin, but I did say that I was hoping there might be a clever trick to exploit the fact that part of my integrand is a first derivative...
Yes, there is! It is precisely the "integration by parts", letting dv= f'(x)dx that you initially did.
 
  • #14
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Thanks, but unless I'm missing something this takes me back to the point I mentioned earlier in the thread: exp(x)*f(x) - Int[exp(x)*f(x), dx], which doesn't really help me due to the complexity of the function f(x).
 

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