Question

help with integration substitution ? Lmao.

Answer 1

is there a question coming, or...?

Answer 2

Hi um i can't find the integral sign on here ? o-o

Answer 3

ill just take a pic of it ok ?

Answer 4

third row in the middle

Answer 5

ok

Answer 6

I wasn't really sure which to substitute is there a trick to know which lol

Answer 7

there is no "trick" in the sense that you can do some method to find the "right" u-sub each time, because you can pretty much always solv the integral with all kinds of different subs, as you'll learn later in calc

the "trick" for finding the best simple u-sub in problems at this level, though, is to look for one part of the expression that is the derivative of another part of the expression times a constant

Answer 8

oh

Answer 9

for instance, if you see \[\int {\ln x dx\over x}\]you can see that you have \(ln x\), times the derivative, \(\frac 1x\)

Answer 10

that would suggest you want to make the substitution \(u=\ln x\implies du=\frac1x\)
and the problem reduces to \[\int udu\]

Answer 11

in your case, what part of the expression looks like the derivative of another part of the expression?

Answer 12

um... lol sorry im really slow is it x^4+1 since it equals the derivative of e^x^5+5x ? lol

Answer 13

yea :)
except it doesn't quite equal the derivative, it equals the derivative times a constant
go ahead and make the u sub and see what you get for du

Answer 14

okay thx ill let you know once i get stuck lol

Answer 15

wait i misread, the x^4+1 is like the derivative of the exponent, x^5+5x
so that means your u should be x^5+5x
now find du and try to substitute

i have to go soon, sorry if i just vanish :P

Answer 16

Okay so far i got 1/5e^udu the x^4 canceled out so im doing something right lol, so now would i just integrate ? so is it 1/5xe^u then just substitute x for u and i got my answer ?

Answer 17

aww you left =/ lol

Answer 18

sorry dude, had a student. you were doing perfect though, just integrate that sucker and there's your answer :)