$\displaystyle \int (ae^{x}-ye^{x})=-ye^{x}+(a+1)e^{x}+c$ this is an interesting technique where you just add (a+1)e^x to find the antiderivative
If you have a complex-valued function of a real variable, you can integrate the real and imaginary parts separately. If you have a function of a complex variable, then you'll need to do a path integral.
In this forum, people post the math problems they're having trouble with (and where they're having trouble), and we give them advice on how to get through the difficult parts.
- Hollywood
thanks! I'm still a math student....I guess this equation has the narrow condition that d/dx[g(x)]=g(x).... anyway in the Braun Differential Equations text he uses the product rule to prove a solution for the nonhomogeneous first order DE. I kind of like the text since he starts with analytical methods. I don't know if this is from Dr. Feynman, but kind of interesting to contemplate
thanks! anyway it's an interesting challenge to try to do integrals after a drink and no sleep. by the way I have another thread on Wrinkled Spheres that you could look at and comment! so you think that Schey is a good book? I am just curious about the thought processes of professional mathematicians or physicists as in equation modeling, do they imagine an expression that they are looking for and which techniques do they use to arrive at the correct equation which in the case of physics I guess correlates with experimental results?