@XanderHenderson Indeed. It's easier to teach face-to-face because the real-time continuous student responses push certain buttons in our head harder than the intermittent sometimes non-existent responses on the internet. =)
Supposing to have these integrals, for example,
$$\int\limits_{-\infty}^{+\infty}\frac{dx}{(x^2+1)^2}=\frac12\left(\arctan x+\frac{x}{1+x^2}\right)\tag 1$$
$$\int\limits_{0}^{+\infty}\frac{x^2}{x^4+1}dx=\sqrt{2}\pi/4 \tag 2$$
$$\int\limits_{0}^{2\pi}\frac{1}{2\cos x+5}dx=\cdots \tag 3$$
They can ...
@XanderHenderson Hi, and thank you for your reply.
@XanderHenderson I am interested in whether there is a bottom-up order of solution, i.e. whether an integral cannot be solved by classical methods when resorting to complex analysis and what needs to be done?
@Sebastiano This room is is meant to help users coordinate action on questions which may need to be closed or reopened, deleted or undelete, or edited. If you are asking us to take one of those actions, please explain.
@In other words, when I can't solve an integral I solve it with numerical methods? With complex analysis, can integrals always be solved in real variables?
@Sebastiano Yes, I see that. Personally, I think that it should have been closed. It is too broad (maybe try to narrow down on a specific class of functions...?), and lacking in details (what do you mean by "the usual mode"?).
@Sebastiano What action are you asking people in this room to take? If you are not asking us to take some action, please seek advice in the room "Constructive Feedback", to which I linked above.
@XanderHenderson I thought you could ask for advice in this room and I didn't think it was the wrong one. Anyway, I'll take your advice and thank you very much.
