I have input this:

Integrate[1, f[t]*Exp[(v/V)*t]]

That is ∫1∗d(f(t)∗evV∗t)∫1∗d(f(t)∗evV∗t)\large\int 1*d(f(t)*e^{\frac{v}{V}*t})

I expected this output:

f(t)∗evV∗t+Cf(t)∗evV∗t+C\large f(t)*e^{\frac{v}{V}*t} + C

but instead I get:

Integrate::ilim: “Invalid integration variable or limit(s) in E^((t\v)/V)\ f[t]. ”

What am I doing wrong ?

PS: in the model at the origin of my troubles t is the only variable v and V are constants

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But I want to integrate 1 with respect to f(t)*e^(v/V*t).

– Ouistiti

Jul 31 ’13 at 12:20

You can want whatever you like, but you have to adhere to the Mathematica syntax. It expects a variable in that position and what you provide is clearly not a variable.

– Sjoerd C. de Vries

Jul 31 ’13 at 12:23

2

Integrate[1, u] /. u -> f[t]*Exp[(v/V)*t]

– gpap

Jul 31 ’13 at 12:28

1

This works thanks gpap do you want to put it as an answer?

– Ouistiti

Jul 31 ’13 at 12:37

1

The type of integral you want to calculate often pops up when using the integration by parts trick. The resulting expression with a function behind the d is considered by many a (slight) abuse of notation and not mathematically solid.

– Sjoerd C. de Vries

Jul 31 ’13 at 12:39

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2 Answers

2

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Well, here’s a (trivial) answer that works:

Module[{u}, Integrate[1, u] /. u -> f[t]*Exp[(v/V)*t]]

FYI: For best style u should be \[FormalU] or localized with Module. (+1)

– Mr.Wizard♦

Jul 31 ’13 at 15:39

agreed and amended

– gpap

Jul 31 ’13 at 15:47

Here’s a way to implement your concept. But you do have to specify which variable is the variable of integration:

SetAttributes[int, HoldAll];

int[integrand_, D[measure_, var_Symbol]] := Integrate[integrand D[measure, var], var]

int[1, D[f[t]*Exp[(v/V)*t], t]]

(* E^((t v)/V) f[t] *)

And

int[f[t] Exp[(v/V) t], D[f[t]*Exp[(v/V)*t], t]]

(* 1/2 E^((2 t v)/V) f[t]^2 *)

Etc.