It seems like I am stuck on such a simple problem:  How to I find the antiderivative of $\cos^2x$? I have tried partial integration, it doesn't seem to work (for me). Some help on how to integrate it would be nice.
Suppose $\displaystyle P(x,y)$ a polynomial in the variables $x,y$.   For example, $\displaystyle x^4$ or $\displaystyle x^3y^2 + 3xy + 1$.  Is there a general method which allows us to evaluate the indefinite integral     $$ \int P(\sin x, \cos x) \text{d} x$$   What about the case when $\displaystyle P(x,y)$ is a rational function (i.e. a ratio of two polynomials)?   Example of a rational function: $\displaystyle \frac{x^2y + y^3}{x+y}$.    This is being asked in an effort to cut down on duplicates, see here:   and here:
Use Outgoing SSH to receive incoming SSH My ISP does not allow me to have a static IP address. As such I am unable to remotely SSH in my home machine. Is there a way I could SSH from my home machine to a server and SSH into the server from my remote laptop and bridge the two connections?  Cheers! Is 1+1 =2 a theorem? A theorem is defined to be a mathematical statement that is proven to be true. The statement $1+1=2$ has definitely been proven in the history of mankind (Russel and Whitehead had once proven it in the book Principia Mathematica).   So can it be considered as a theorem? What determines something to be a theorem (besides it being proven to be true)? Prove holomorphism of expression I have to prove that given $\gamma$ contour of $G \subset \mathbb{C}$  and $f$ continuous function on $G$. Then the function $g(z) = \int_{\gamma} \frac{f(w)}{w-z}dw$ is holomorphic on $\mathbb{C} - \bar{G}$ My attempt: I started by using that given any parametrization $\alpha :[a,b] \rightarrow \gamma$ we can rewrite $g(z)$ as: $g(z) = \int_a^b \frac{f(\alpha(t))}{\alpha(t)-z}\alpha'(t)dt$ Now using the fundamental theorem I derivate to see where $g'(z)$ is defined and I get: $g'(z) = \frac{f(\alpha(b))}{\alpha(b)-z}\alpha'(b) - \frac{f(\alpha(a))}{\alpha(a)-z}\alpha'(a) $ Here I get stuck, I fail so see how this links back to $g$ being holomorphic at $\mathbb{C} - \bar{G}$. Any hints on how to proceed? Thanks! Stop generating "possible duplicate" comments When a question has pending close votes, the system now adds a banner indicating that the question might be a duplicate:    But the first user to vote still generates a possible duplicate comment:    Those comments were always a hack, just like editing the link into the top of the post. The banner eliminated the need for the latter; can we stop generating those comments too? Cross product term in linear regression why is it zero I'm trying to see why this is the case. I have taken  the LHS and added $X\hat{\beta}$ and subtracted $X\hat{\beta}$.  From this I can get both terms on the right but I end up with a cross product term  $2(y-X\hat{\beta})^T(X\hat{\beta} - X\beta)$  that I can't prove equals to zero. I think there is some trick I'm missing, anybody remember it? Do Nigerian citizens need a transit visa for Brazil? Do I need a transit visa in Brazil on the way to Ecuador. I am a Nigerian national.   I am travelling to ecuador and I was asked to get a Brazilian transit visa as I am to board another airline from Sao Paulo. Is short-circuiting logical operators mandated? And evaluation order? Compare means of group with a mean of a subgroup A Regular Tetrahedron is a cool Polyhedron. A regular tetrahedron has this property:  For any two of its vertices exists a third vertex, which forms a regular triangle with these 2 vertices.(It doesn't necessarily have to be a face of it).  Are there any other polyhedrons that have the same property?  I think there isn't such a polyhedron. But not sure how to prove it. I've tried proving that there isn't an irregular tetrahedron with this property, assuming that there is a pair of unequal sides.   Current answers are a little confused with the conditions of the problem. What is the advantage of using wp_mail? What is the advantage of using wp_mail() over mail(). Codex says they're similar, but they seem to be very similar. Make apt-get (or aptitude) run with -y but not prompt for replacement of configuration files? When running apt-get -y install &lt;packages ...&gt; on Ubuntu 10.04 I would like apt-get (or aptitude if that makes it easier) to not prompt me when installing additional dependencies (behavior of -y as I understand it) and but not prompt me about overwriting configuration files, instead assume to keep the existing ones always (which is usually the default). Unfortunately --trivial-only seems to be the inverse of -y and not affect the prompt that is shown, according to the man page.  In particular packages auch as samba, nullmailer, localepurge and lighttpd have forced me to interact with the terminal, even though the whole procedure was scripted and meant to be non-interactive. Seems that I just proved $2=4$. Prove that if $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m &lt;n.$   Since $G$ is of prime-power order I know $|Z(G)| \ne e$ so there is an $a\in Z(G)$ with order $p$ such that $p \mid |Z(G)|$. Now, the subgroup generated by is normal since it's a subgroup of the center. How can I get this normal subgroup to be less than $n$? Can I use my laptop as a second monitor? RMSE vs Standard deviation in population Do I need to upgrade RAM from 4GB to 8GB for Android development? I'm an android developer and have laptop with 4GB RAM. When I compile my project the RAM is used at 100%.    If I add more RAM will it solve the problem? In first.bat, I use  var5=C:\Program Files (x86)\Microsoft Visual Studio 10.0\VC\bin\x86_amd64\ CALL scripts\vc64.bat %var5%   And in scripts\vc64.bat, I use  SET var6=%1vcvarsx86_amd64.bat CALL %var6%   But I get : 'C:\Programvcvarsx86_amd64.bat' is not internal or external command..... error.  If the path assigned to var5 has no space, then it is fine.  I tried several combination of quotations and %1vcvarsx86_amd64.bat, but no change.  How do I make it works with path with spaces?    To be more precise, suppose it is C:\a b c\  In first.bat:       SET var6=C:\a b c\  =====&gt;  '"C:\avcvarsx86_amd64.bat"' is not.....`      SET var6="C:\a b c\" ====&gt;   There should not be a b      SET var6=C:\a\ b\ c\ ====&gt;    Can't find the specified path      SET var6=C:\a b c\ + Using "%var6" ====&gt; There should not be a b     Update: Here is an example. Change a b to ab works.  call.bat in C:\  @ECHO OFF  SET var5=C:\a b\ CALL C:\1.bat "%var5%"  pause   1.bat in C:\  @ECHO OFF  SET var6=%~1Test.bat CALL %var6%  RMDIR /S C:\NoWorry   Test.bat in C:\a b Test.bat in C:\ab  @ECHO OFF  RMDIR /S C:\ThereIsNoSuchFolder Can we have a way to access Area 51 on the iOS and android app?  More sites would flourish due to more traffic. How to get rid of the smell from the fridge? The Crossbow Expert feat gives three benefits, the first of which is explicitly tied to crossbows and the last of which to only hand crossbows. But in the middle, there is:     Being within 5 feet of a hostile creature doesn't impose disadvantage on your ranged attack rolls   Notably missing is a qualifier like "when attacking with a crossbow". Does this mean that the benefit applies to other ranged weapons and to spells which require ranged attack rolls? Or does the name of the feat itself limit this to  crossbows?