Integrating the product of an exponential and a first derivative

[bventer]

Hi, besides integration by parts, does anyone know of a simple integration trick to solve the integral (wrt x) of exp(x)*f'(x)?

 

[Mentallic]

Could you show me how it's done by integration by parts?

 

[bventer]

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?

 

[JJacquelin]

that doesn't really help me due to the complexity of the function f(x).

Why not showing us what is f '(x) ?

 

[Mentallic]

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 e^xf(x).

I can't think of another way to show it besides that technique, maybe someone else can.

 

[bventer]

To JJacquelin: I you wish, see attached jpg (apologies, but I am not well versed in Latex)

 

[bventer]

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

 

[Mentallic]

To JJacquelin: I you wish, see attached jpg (apologies, but I am not well versed in Latex)

How is the y(H) function defined?

 

[bventer]

How is the y(H) function defined?

y(H) is a quadratic: a0 + a1*H + a2*H^2

 

[JJacquelin]

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.

 

[bventer]

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...

 

[JJacquelin]

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.

 

[HallsofIvy]

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.

 

[bventer]

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).