When WolframAlpha is confused by the complexity of my query I have sometimes had success solving part of the problem first and then giving it the rest of the problem as a second query.
First I try to find the integral with the appropriate constants, but not defining x to be a constant. I think WA has understood that the symbols are numeric constants and not units.
Find the integral
Then I use the result of that to try to complete the problem
Find the value of v
I worry that I have misinterpreted your problem because of the complex number as a result.
Perhaps you can see how to adapt this technique to solve your problem correctly.