Not looking for a solution yet but what would your first step be to integrate $$\frac{x-1}{\sqrt{x}+1}$$ Clearly I have to sort out that nasty denominator.
@BalarkaSen How about this one $$\lim_{n\to\infty} \frac{ \int_a^b f^{n+1}(x) dx }{ \int_a^b f^n(x) dx }$$ where $f:[a,b] \to [0,\infty)$ is continuous and $f\neq0$
== English ==
=== Etymology ===
This saying was coined by Anne Isabella Thackeray Ritchie (1837–1919) in her novel, Mrs. Dymond (1885):
"I don't suppose even Caron could tell you the difference between material and spiritual," said Max, shrugging his shoulders. "He certainly doesn't practise his precepts, but I suppose the Patron meant that if you give a man a fish he is hungry again in an hour. If you teach him to catch a fish you do him a good turn. But these very elementary principles are apt to clash with the leisure of the cultivated classes. Will Mr. Bagginal now produce his ticket...
Ah, mathematics stack exchange. Closing and downvoting a question equivalent to this one mathoverflow.net/questions/78771/… . Only took about a minute. (The question on MO has 1 sketchy answer by an expert).
@JasperLoy Sorry for late answer - I'm not, I'd be ashamed with these questions if I was. I have a first degree in computer science from around 15 years ago, and I'm about to do a second degree in business. Despite me getting 740 in GMAT, I'm forced to do "prerequisite" courses in maths, statistics, and economics, just to be allowed to take certain courses within the degree itself
@BalarkaSen The author has a beautiful solution to the problem I sent you earlier. I have written it down in my own words to memorise the strategies he used
BTW, I want to ask something that's why I log in to chat room. Does anyone here know who is user: Marvis? He is very good at calculus but his account is not active anymore.
@V-Moy He answered some of my questions in the past. He's a very clever person, gave many good answers, but I think he deleted his account for some months. Btw, are you Marvis? :-)
@V-Moy It won't ruin your day. That user's modus operandi is to downvote closed questions so that they're deleted. That user doesn't downvote people because he/she is angry at them.