# 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)?

Last edited:

Homework Helper
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) ?

Homework Helper
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.

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

#### Attachments

• f(x).JPG
15.7 KB · Views: 409
bventer
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

Homework Helper
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.