Question

Hello there having some trouble with some integral quesitons. Help appreacited and medal of course. Will post below

Answer 1

Find the derivative of \[F(x)=\int\limits_{\ln(x)}^{\ln(x+1)}2\sinh(t)dt\]

Answer 2

So i try doing the question using the fact that sinh=\[(e^x-e^-x)/2, \] so the 2 will cancel, then I try using the fundamental therom and chain rule but it still isnt working.

Answer 3

Any insight would be great, thanks

Answer 4

i would say \(\sinh(\ln(x+1))\times\frac{1}{x+1}-\sinh(\ln(x))\times \frac{1}{x}\) although there might be a slicker way of writing it

Answer 5

damn i forgot the \(2\)

Answer 6

oh your method is much better

Answer 7

Hey yea well I know the answer is given as 2x+1/(x)^2(x+1)^2 but I cant seem to get it into that form

Answer 8

lets try it

Answer 9

\[\frac{e^{\ln(x+1)}-e^{-\ln(-x-1)}}{x+1}\] for the first part

Answer 10

that gives
\[\frac{x+1-\frac{1}{x+1}}{x+1}\]

Answer 11

damn i made a typo above, but the second part is right

Answer 12

second part will be
\[-\frac{x+\frac{1}{x}}{x}\]

Answer 13

then i guess a raft of algebra

Answer 14

first line should have been
\[\frac{e^{\ln(x+1)}-e^{-\ln(x+1)}}{x+1}\]

Answer 15

Correct!

Answer 16

lol thanks

Answer 17

no way i can do all the algebra on the fly, but did you get as far as \[\frac{x+1-\frac{1}{x+1}}{x+1}-\frac{x+\frac{1}{x}}{x}\]?

Answer 18

Yea thanks for the help. I guess that answer would be accepted anyways

Answer 19

algebra from here on in
remove the complex fractions, then subtract