Integrate $\int \frac{x^2}{(x \sin x + \cos x)^2}dx$ Integrate $$\int^{\pi/4}_{0} \frac{x^2}{(x \sin x + \cos x)^2}dx$$  How can I integrate this ?   Question asks us to re-arrange the numerator
Evaluating this integral $ \small\int \frac {x^2 dx} {(x\sin x+\cos x)^2} $ The question:      Compute$$ \int \frac {x^2 \, \operatorname{d}\!x} {(x\sin x+\cos x)^2} $$   Tried integration by parts. That didn't work.  How do I proceed?
How to exclude files from Visual Studio compile? I'm in the process of refactoring a project.  I've got an entire subfolder which is known to be broken.  Is there any declarative way to exclude that folder from the compile temporarily while I test the refactoring thus far?  I realize I could delete the folder, but I'd like to do this through configuration if possible. I can't seem to find an answer to this simple question, which I need for some compliance documentation.    On a default install of CentOS 6.5 (OpenSSH 5.3p1-94.el6), after how long of being idle will a user's SSH session be terminated?  I believe the following can be set to increase the idle timeout, but they are commented out by default.  $ grep -i alive /etc/ssh/sshd_config #TCPKeepAlive yes #ClientAliveInterval 0 #ClientAliveCountMax 3   Also, is there a command to dump a list of the current sshd settings?  I don't see anything in man sshd. What is the difference between ANSI/ISO C++ and C++/CLI? FME - Calculate distance of point along a line I have created an FME workspace which inputs a pipeline as well as other linear features which cross it (waterways, roads, railways, fences, other pipelines, etc).  The output is a point file which contains the crossing type.  What I would like to do is calculate the distance along the pipe from the start of the pipeline for each intersection.  So, as you travel along the pipeline, the distance attribute will increase.   I'm thinking that I'll need to use some of the linear referencing tools like MeasureGenerator, MeasureExtractor, or something like that, but I'm not sure how to do so.  Does anyone have an idea of how to do this? In my work, we are comparing predicted rankings versus true rankings for some sets of data. Up until recently, we've been using Kendall-Tau alone. A group working on a similar project suggested we try to use the  instead, and that they preferred it. I was wondering what the differences between the different rank correlation algorithms were.  The best I've found was , which claims Spearman is used in place of usual linear correlations, and that Kendall-Tau is less direct and more closely resembles Goodman-Kruskal Gamma. The data I'm working with doesn't seem to have any obvious linear correlations, and the data is heavily skewed and non-normal.  Also, Spearman generally reports higher correlation than Kendall-Tau for our data, and I was wondering what that says about the data specifically. I'm not a statistician, so some of the papers I'm reading on these things just seem like jargon to me, sorry. where instance variables get initialized I think it would make sense to split up the flag "This is not an answer" into three flag choices:   This should be a comment This should be an edit This should be a new question   If we had that, it would make it easier (and therefore more efficient) for mods to figure out what to do with answers flagged thusly. Number of normals from a point to an ellipse From a typical point $P$ inside an ellipse, how many points $Q_i$ on the ellipse have $PQ_i$ normal to the ellipse?  Someone asked me at school many years ago but I don't think I worked it out. Visit to US before F1 using the Visa Waiver Program I am going to start a phd at the US with an F1 visa. University told me that I could enter the US only 30 days before the date on I-20. Since English is not my first language (and this would be a big change in my life) I would like to go there by June.  The thing is that I have an European passport with a valid ESTA. My plan would be to arrive with this passport, stay 4-6 weeks , go to Canada for a short vacation (maybe flight maybe by land) and come back to the USA with F1 visa.  I have two questions about this:  1) is this possible?   2) If yes, how could I justify knowing I will lose my come-back flight during my first entry? (I would purchase round trip because one-way are too expensive, probably with less than 90 days difference) Object on curve wont stay flat! Command for creating a directory and navigating into it directly? Quite often I need to perform this two commands:  mkdir abc cd abc   I am curious whether there is a simple command (or an alias that I can create and use) to do it in one go, like  user@GROUP:~$ mdcd abc user@GROUP:~/abc$   Is this possible? Satisfying explanation of Aristotle's Wheel Paradox. The paradox:    We have a circle and there is another circle with smaller radius. They are co-centeric.  If circle make full turn without sliding, both smaller and bigger circle make full turn too. If we assume that the passed road is equal to the circumference of circles. We have got smaller circle's radius is equal to bigger one's.  Unsatisfying Solutions I found:    "Do not assume that smaller circle's circumference is equal to passed road since the surface that contacts to the ground is bigger one. " // Okey but it does not explain the paradox, it explains just what is the wrong assumption (even does not explain why it is a wrong assumption.) It is undeniable that every point on both smaller and bigger circle will contact exactly one and only one point on their path. Therefore we can think that this is a bijective maps and smaller circle is isomorphic to bigger one. (Okey but ....)   Question: What is the true answer? What is wrong with the definition of circumference of a circle and relationship with its taken path. Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$? $m$ is the Lebesgue measure. I was thinking that: $\Bbb Q$ is dense and $m(\Bbb Q)=0&lt;1$ but it fails to be open, but maybe I could construct an open set from this fact, or also using that $(0,1)$ is a dense and open subset but $m(0,1)=1$.   Any hints or ideas will be very appreciated. Thanks. Derivative of function with 2 variables I've leart in Calculus 1 that the derivetive of $f(x)$ is:  $$\lim_{h\to0} \frac{f(x+h) - f(x)}{h}$$.  suppose $f(x,y)$ is a function with 2 variables,  does $$f'(x,y) = \lim_{h\to0} \frac{f(x+h, y+h) - f(x,y)}{h}$$ ?  If not , what is the derivetive of function with 2 variables? I have a trained logistic regression model that I am applying to a testing data set. The dependent variable is binary (boolean). For each sample in the testing data set, I apply the logistic regression model to generates a % probability that the dependent variable will be true. Then I record whether the acutal value was true or false. I'm trying to calculate an $R^2$ or Adjusted $R^2$ figure as in a linear regression model.  This gives me a record for each sample in the testing set like:  prob_value_is_true         acutal_value    .34                          0    .45                          1    .11                          0    .84                          0     ....                        ....             I am wondering how to test the accuracy of the model. My first attempt was to use a contingency table and say "if prob_value_is_true > 0.80, guess that the actual value is true" and then measure the ratio of correct to incorrect classifications. But I don't like that, because it feels more like I'm just evaluating the 0.80 as a boundary, not the accuracy of the model as a whole and at all prob_value_is_true values.  Then I tried to just look at each prob_value_is_true discrete value, as an example, looking at all samples where prob_value_is_true=0.34 and measuring the % of those samples where the acutal value is true (in this case, perfect accuracy would be if the % of samples that was true = 34%). I might create a model accuracy score by summing the difference at each discrete value of prob_value_is_true. But sample sizes are a huge concern here, especially for the extremes (nearing 0% or 100%), such that the averages of the acutal values are not accurate, so using them to measure the model accuracy doesn't seem right.  I even tried creating huge ranges to ensure sufficient sample sizes (0-.25, .25-.50, .50-.75, .75-1.0), but how to measure "goodness" of that % of actual value stumps me. Say all samples where prob_value_is_true is between 0.25 and 0.50 have an average acutal_value of 0.45. Is that good since its in the range? Bad since its not near 37.5% (the center of the range)?  So I'm stuck at what seems like should be an easy question, and hoping someone can point me to a resource or method to calculate an accuracy stastic for a logistic regression model. How do I convert Word smart quotes and em dashes in a string? How to prove this sequent using natural deduction? How do I prove $$S\rightarrow \exists xP(x) \vdash \exists x(S\rightarrow P(x))$$ using natural deduction? Just an alignment of which axioms or rules that one could use would be much appreciated. Drop rates for set / legendary items Just wondering what the drop rates were for Set / Legendary items, or is it totally random? I imagine they would increase for later acts in Inferno. My monk is comfortable in Act 3 in Inferno, but I've only found one set item, so MF will increase chances for them? Show that if a function is not negative and its integral is $0$ than the function is $0$ Suppose $f$ is continuous, $f(x) \ge 0$ on $[a,b]$ and $\int_a^b f(x) dx=0$. Show that $f(x)=0$ on $[a,b]$.   I know that if $f$ in continuous at $x_0$ and $f(x_0) &gt; 0$, then there exists $\delta &gt; 0$ s.t. $f(x) \ge \frac{1}{2} f(x_0)$ for $|x-x_0| &lt; \delta$ and I think it should help me but I'm stuck at this point. Ubuntu MATE freeze on logout/shutdown/reboot when running on Intel graphics card