Using differentiation under integral sign evaluate $\int_{0}^{\frac {\pi}{2}} \ln (\frac {a+b\sin x}{a-b\sin x}) \cdot \frac {dx}{\sin x} $ My Attempt: Given $$\int_{0}^{\frac {\pi}{2}} \ln (\frac {a+b\sin x}{a-b\sin x}) \cdot \frac {dx}{\sin x}$$ Let, $$F(a)=\int_{0}^{\frac {\pi}{2}} \ln (\frac...
EDIT: Now there is question discussing tags for specific inequalities in general: Which (if any) inequalities with real numbers should have separate tags? The tag a.m.-g.m.-inequality has been created recently Is this really going to be useful? It seems a bit too specific to me. In any case, i...
There are certainly many inequalities which are rather important and useful and which appear frequently in various areas in mathematics (AM-GM, Jensen, Cauchy-Schwarz, etc.) The question I want to ask is whether some of them would be also useful as tags on this site. And if yes, for which of them...
Not long ago, we had to adapt to the circumstances at hand regarding the changes to how close reasons were displayed. You can read more about this here. We now have other changes. A good place to read about it is here. To summarize: the “Off-topic” banner has been replaced with “A community-spe...
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