I need help finishing an integration by parts problem that I've already started. I think my substitutions for u and dv are good, but I'm still stuck. I've scanned a copy of my work and I attached it to this post. Can someone please take a look at it and tell me what I'm doing wrong and/or what I need to do next?
Thank you.
it's just a common trick that is used. i added 1 and subtracted 1 in the numerator *that way, it's like adding zero, so i am not changing anything). doing that allows me to simplify the way i did. now i could split the fraction into two fractions. one simplifies to 1 which is easy to integrate, the other simplifies to a fraction that is easily taken care of by substitution
Hey. I need more help. I used the same technique of adding 1 and subtracting 1, but this time it doesn't work out as nicely as it did for the last one.
I posted an attachment of my work again. You should just ignore the last part because I don't think that it makes any sense.
apparently i gave you the impression that adding and subtracting 1 ALWAYS works. that is not the case, it depends on the particular integral. examine the integral i used that technique on and the integral you attempted to use it on, notice any differences? don't try to just mindlessly absorb and apply techniques, look for the reasoning behind them. as Soroban rightly pointed out, your last integral was an easy substitution problem. You do not have to always add and subtract 1 (in fact, in some cases you have to add and subtract 2, or 3, or 7 or whatever, or multiply and divide by the same thing etc). do what is called for. the above mentioned techniques are only applied when we want to change an ugly integral where none of our old techniques work, into a nice integral where at least one of our techniques work. the integral you attempted to use it on did not require it, it was already a "nice" integral, where one of our old techniques (substitution) works