Use integration by parts to calculate 𝐼 =   f  e^(ax) cos 𝑏𝑥 𝑑𝑥 for 𝑎 ≠ 0 and 𝑏 ≠ 0.  This is my working so far. The part where i have to integrate is confusing so with some help maybe i can do it .
I am curious about the proof of these two integrations. It would be great if you could point me in the right direction : $ \int{e^{ax}\cos({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\cos(bx)+b\sin(bx)] + C $ &amp; $ \int{e^{ax}\sin({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\sin(bx)-b\cos(bx)] + C $
I have FlexiPage Home_Page_Default.flexipage assigned as Default Home Lightning Page for all profiles in one sandbox. I need to migrate it to another sandbox and assign as Default Home Lightning Page for all profiles in the destination sandbox.   I am able to retrieve and deploy that flexipage but looks like I am not able to assign it automatically as Default Home Lightning Page for all profiles in the destination sandbox using Force.com ANT Migration Tool or changeset.  Is that possible to migrate default home flexi page assignment from one organization to another using ANT Migration Tool or changeset?  If this is possible then how? mysqli bind_param for array of strings Favorite Tag Buttons partly sticking off page I appear to have found a bug, when adding Favorite tags, I find that the buttons are half off the page (this is of the  site):    Although on other sites it looks more like this:    I am running Ubuntu GNOME 15.04 with Firefox 41.0.1+build2-0ubuntu0.15.04.2. Is it legal to run windows on a mac? I understand that it is Illegal to run OSx on a windows machine or PC for that matter, but is it illegal to do the reverse? Why or why not? My primary server with SQL Server 2005 broke down, so I've started up the log-shipped database on the secondary server. The database is live on the secondary server, and I just need to remove the log shipping settings for it, while the primary server is no longer accessible.  It seems that the sp_delete_log_shipping_secondary_database stored procedure should be executed on the secondary server to do this, which "removes a secondary database and removes the local history and remote history", as it is stated on .  Would this also remove the database itself? Or only the log shipping settings for it? And what will it do when the primary server is not accessible?  I must not loose the database on the secondary server, as it is already in use. Canonical vs. non-canonical terminal input I am studying for an exam and I am confused as to how canonical vs. non-canonical input/output works in Unix (e.g., curses).  I understand that there is a buffer to which "line disciplines" are applied for canonical input.  Does this mean that the buffer is bypassed for non-canonical input, or does it simply mean that no line disciplines are applied?  How does this process differ for input and output operations?  In the curses programs I have worked with that demonstrate canonical input, the input typed by a user is automatically entered either after a certain number of characters have been typed or a certain amount of time has passed.  Are either of these things considered "line disciplines" or is this something else entirely? Probability of winning the game "1-2-3" When approximating a posterior using MCMC, why don't we save the posterior probabilities but use the parameter value frequencies afterwards? What is the use of the Dot Product of two vectors? What is the definition of a symmetric distribution? Where to start with the Star Wars books? Modern movie where rich people can buy a personal assistant that sit in a small egg This is a modern movie and rich people can buy this egg with a personal assistant. It's an actual person in it (or a person's mind). I believe it can even operate a toaster.  I believe later in the movie, a person (or their mind) can be transferred to such an egg. As a punishment, they increase the speed of time inside that egg to make the person inside the egg bored to death, so to speak. I know that IList is the interface and List is the concrete type but I still don't know when to use each one. What I'm doing now is if I don't need the Sort or FindAll methods I use the interface. Am I right? Is there a better way to decide when to use the interface or the concrete type? Find longest repeating string based on input in perl (using subroutines) A question of Euclidean domain Simple way to understand what derivative is I know how to count derivatives, but I actually don't understand what are those? What do they show?   Wikipedia explanation: Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity. I understand nothing what is written here?  Please, if you can, explain me as simple as you can it. Thank you very much. The Drupal 8 REST UI configuration page asks me to select Authentication providers for GET method; otherwise, it doesn't allow me to export the REST request.  How can I provide anonymous user to access my REST GET API without providing any auth information? Double integral with transformation; possible error in limits I'm asked to show that the following integral is true with the transformation $u = x+y$ and $y=uv$:  $$\int_0^1 \int_0^{1-x} e^{y/(x+y)} dx dy = \frac{e-1}2 $$  I found the determinant of the jacobian of the transformation is $-u$, and the exponent is just $v$ so the integral becomes $$\iint_R |-u|e^v du dv = \frac {u^2}2 e^v|_R$$ $$=\frac{(x+y)^2}2e^{y/(x+y)}|_{x=0}^{1-x}\;|_{y=0}^1$$ And plugging it all in doesn't work (AFAICT). For one, the x's don't all cancel.  I've looked at it 100 times. It's definitely written dxdy not dydx even though there is definitely an x in the integral. Maybe this is a typo and why my calculation isn't working out? I tried reversing the order to dydx and it didn't work. I tried changing the limit of integration to $1-y$ and it didn't work out.  I'm not even sure how to figure out the domain of integration in the uv-plane. Flipping things around yields y=uv and x=u-uv. But if my domain is bounded by x=0 and y=0 and y=1 (ignoring the last limit for now), then I have uv=o=u and uv=1. !?!  Am I just making an algebra mistake plugging everything in? Is there a way to handle a variable in it's own integral that I'm unaware of? I want to executed command from file (which is script) in current shell in terminal.  Example: I have file ch_dir contains following:  #!/bin/bash cd /usr   Now if I execute file usually as following then it executes commands in different shell:  pandya@pandya-desktop:~$ ./ch_dir pandya@pandya-desktop:~$   Here cd /user is executed in different shell.  But I want to execute in Current shell. How do I do that?  Note: Here cd is only used to explain. Question's aim is to execute any command in current shell bash regex with quotes? The following code  number=1 if [[ $number =~ [0-9] ]] then   echo matched fi   works. If I try to use quotes in the regex, however, it stops:  number=1 if [[ $number =~ "[0-9]" ]] then   echo matched fi   I tried "\[0-9\]", too. What am I missing?  Funnily enough,  suggests this should work.  Bash version 3.2.39.