I would like to find the closed form of:  $$\int_0^{\pi/2} \frac 1 {1+\tan^{s} x} \, dx$$  I have tried substitution method, $t=\tan (\frac{x}{2})$ Then I ended up with with a very complicated rational function in the integrand.   Can anyone help?
Evaluate the integral $$\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$$
US Salary Transfered to Indian Acc and Tax Relation I am on an H1b visa working and receiving a salary in the US. I have transferred approximately $15-20k to my account in India Account (not an NRE account).    How would this transfer affect my taxes in US and India. How can I avoid tax on the money that I have transferred. Would any investments help save taxes? Do I need to declare anything? If so, where ? What is the best way to add options to a select from a JavaScript object with jQuery? How do the Treasure Goblins work? Every once in a while I'll come across the sneaky devils and they always flee.  What determines when they flee (time, distance, etc.) and do I get better loot by killing them faster?  Is there anything else I should know in order to get the most out of the encounter?  EDIT: What I mean is: Is the final drop better based on how effectively I defeat them? What is the meaning of $\exp(\,\cdot\,)$? What is the meaning of the notation $\exp(\text{expression})$ ?  I think that it's something of the form $a^\text{expression}$ but does it mean that the base $a=e$ or can it be any base? Do I have to enter the UK on my UK passport? I'm a British National (Overseas), which basically means that while I don't have the right of abode in the UK, I am permitted to visit the UK without a visa. However, my passport has expired, and while it's being renewed, the schedule is a bit tight.  At the same time, I'm an US Citizen, and since I'm only planning to visit the UK, I don't need a visa if I enter on my US passport.  I'm not familiar with UK immigration law, and given that this probably isn't too common a situation, the UK Border Agency website doesn't have an answer that I can can find, nor do they seem to have a contact form that fits my situation, so here's hoping someone knows—given that I'm a British National (Overseas), am I required to enter the UK on my UK passport, or can I just use my (valid) US passport? Should there be a place to ask about programming libraries and technologies? Mechanics around a rail tank wagon How to place text above the figure/table How to place text above the rotated Figure (LANDSCAPE) in the same page. I tried but text automatically moved to the following page.  TEXT TEXT....   \begin{landscape} \begin{table}[] \centering \includegraphics[width=160mm]{figures2/comparation3.png} \caption{A comparison of Aloha protocols} \label{tab:ComparationAloha} \end{table} \end{landscape}     I added this code, but one part of table disappeared. I must have type TABLE since I need it for list of tables later.  \lipsum[11] \begin{table}[h!] \rotatebox{90}{\parbox{100mm}{ \includegraphics[width=160mm, rotate=90]{figures2/comparation3.png} \caption{A comparison of Aloha protocols} \label{tab:ComparationAloha}}} \end{table} \lipsum[12] Simultaneously merge multiple data.frames in a list When is unbalanced data really a problem in Machine Learning? We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem. Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$ $\sum_{n=1}^\infty n*(n+1)*x^n$  Hello everyone,  I need help in solving the question above.  I started with $\frac{1}{1-x} = \sum_{n=0}^\infty x^n$, if differentiated it once so it became $\frac{1}{(1-x)^2} =\sum_{n=1}^\infty nx^{n-1} $ but from here I don't know how to continue. Thanks. Changing underline color of LanguageTool in TeXstudio I've recently installed LanguageTool to check grammar and spelling mistakes in TeXstudio. However, I often miss the errors because the gray-bluish underlining makes them hard to spot. Is there a way to change the underlining to a distinctive color, such as red for example?   I checked . It says I have to do some changes to the .languagetool.cfg file, but for some reason this file doesn't appear in File Explorer. Forcing Subdivide to create non-zig-zag edges get exact file create time windows 7 I'm trying to figure out exactly when I created a file. Windows 7 thinks I don't know how to subtract two times, and tells me it was created "1 hour ago." I need a little more detail than this, but I can't seem to find a setting to toggle this "feature" off.  Example below: Is there any "official" guidance to upgrading from Lubuntu 18.04 LTS (LXDE) to Lubuntu 18.10 (LXQt) Is there a way to buy SO reputation? Quick question about curly braces not showing up Ii am writing a short code, so I doubt anything else in the code is causing the problem. This is the problematic line of code:  \[ M_R := \max {|f(z)|: |z - z_0| = R }\le M\]   It doesn't show the curly braces. I've tried using \left{ and \right} but to no avail.  What should I do?  Thank you A few years ago, I applied for a UK visa. The visa was initially refused and I had no rights of appeal. However, the refusal letter had some glaring mistakes and I sent an email to the Embassy. The refusal was "overturned" by an ECM.  I am now making an application for a visa which has the question "Have you ever been refused a visa?". How should I answer it? Testing a UPS by unplugging it from the wall Travelling within the US as a foreign citizen without a passport I'm travelling within the US and am a British citizen. Can I travel without my passport and just show my UK driver's license instead?