I suck at integrals. , it says that $$\int \mathrm{e}^{cx} \sin bx \,\mathrm{d}x = \frac{\mathrm{e}^{cx}}{b^2 + c^2}(c \sin bx - b \cos bx),$$ which is easy to check – but how could I have derived that?
Is there a general formula for finding the primitive of $$e^{ax}\sin(bx)?$$  I've done this manually with $a=9$ and $b=4$ using Euler's formulas. But it takes a bit of time. Is there a pattern here?
This is in Windows, but answers for other operating systems can be handy to others.  Most guides say something to the effect of "hold down the Alt key and type in the code on the keypad".  This works fine for decimal codes (like 65 for 'A'), but not for  codes (like  for 'A').  Some applicatons provide other facilities that will allow hexadecimal Unicode character codes to be typed and then transformed.  Word allows you to type the code (such as 200f) and then convert it to Unicode by typing Alt-X.  I'm looking for a general method of doing this that will work with the standard input. Stack Overflow has left! Correct usage for "all you need is/are..." How do I install transition molding between my new hardwood and existing tile floors? I have ripped out some old carpet and am preparing to install a new solid hardwood floor myself.  In several places, the floor transitions to an existing tile floor.  The hardwood floor guys told me the best transition between the two is a T molding.  You simply leave a gap between the two floors, and then place down the T molding between the two floors, so it sits on both surfaces.  Sounds simple enough.  However, the height difference of the two floors is considerable, and the T molding does not sit flush.  What are my options?  Here is a diagram showing the dimensions.      NOTE:  Using the T molding is not a requirement, I could go some other route if there is a better option. Easiest way to move my Windows installation to an SSD? I've taken the plunge and bought an SSD and want to move my existing Windows installation over. The current hard disk is 500Gb, but I've trimmed the contents down to about ~40Gb. I'm transferring it across to a 100Gb SSD and looking for the easiest way just to copy everything across and set the SSD up as a boot device.  I've looked at a few tools like Macrium Reflect, but they don't seem able to restore to a smaller drive. Do I need to go for something like  to do this? I'm trying to avoid scary Linux-based boot utilities if possible, does anyone know of an easier way? Restoring default toolbar layout in Blender 2.81 I would like to open all chapters of my PDF ebooks in the same window but neither evince nor okular seems to be capable of doing that (at least not out-of-the-box).  Is there a way to work this out? How not to show Universal Access menu Icon in task bar in Ubuntu 18.04? Expand the username auto-completion to everyone who can be notified Unlock by fingerprint only Born's Rule, What is the Reason? I'd like to know how I can recursively (edit: iteratively) compute variance, so that I may calculate the standard deviation of a very large dataset in javascript. The input is a sorted array of positive integers. What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the . What is the command that lets me see what and where devices are mounted?  I'm having trouble changing songs on my old iPod, and I have a feeling it's because of the mount point. Splitting lines with points while maintaining other dissolved lines? I am on ArcGIS Desktop 10.2. I have a line feature class of a stream network. I also have a point feature class along the main stream (line) where a catchment enters that stream. I have dissolved my whole streams layer into one line feature and want to split this feature at the points.    However, when I use the  tool, the lines that don't have a point splitting them are still being split at the intersection of two streams.    Why did this line not stay as one feature with the other lines on that side of the splitting node and how can I prevent this from happening? I would like to install Ubuntu 14.04.02 LTS on my machine which currently has Mageia 4.1.   So, I have the following partitions: One for /, one for swap and one for /home.   I have some important data on /home which I wouldn't like to lose (I have backed them up, but I would prefer to keep them) after a clean install. I plan to reformat partitions one and two as above and keep the /home one.   Will I be able to tell Ubuntu to do so during an installation? By this I mean: Will it be able to recognize the /home partition and keep all its data intact while formatting the rest? And one more question: Will it be able to keep the users as they are our will I be forced to change them too? (I have the bad feeling that it won't be able to keep the users as they are...) Changed permissions of / to user Can the off-regional pokémon hatch from eggs? Some people claim you can get the pokémon that are not in your region from eggs. Is this only a rumour or actually true? I've seen off-regional pokémon in gyms nearby but I can't rule out that the owner had been abroad or maybe even used location spoofing. Should we have a tag for significant points in time? I remember coming across this fact a while ago in a pdf somewhere, but I haven't been able to find it again. Can someone show me how to prove it? I would appreciate easier proofs.  EDIT: I'm very sorry, I forgot to actually state it.  Prove that $-1$ is not a quadratic residue modulo primes of the form $4k+3$.  Thanks!