Question

Hard Calculus Problem.

Answer 1

\[\int\limits_{?}^{?} e ^{x}(1+e ^{-2x})\]

Answer 2

Substitution will do..

Answer 3

Let \(e^x = t\)..

Answer 4

\(e^x \cdot dx = dt\)

Answer 5

They left a hint saying multiply it out

Answer 6

But lets try your way

Answer 7

Let us try both. :P

Answer 8

i was gonna suggest expanding it as well ...

Answer 9

Can you show that way please

Answer 10

\[e^x(1+e^{-2x})\]
\[e^x+e^{-2x+x}\]
\[e^x+e^{-x}\]

Answer 11

\[\int\limits(e^x(1+ e^{-2x})) dx = \int\limits (1+ t^{-2})dt\]

Answer 12

Then what amistre
and continue only to chat

Answer 13

yeah I know Mods are quite faster than me..

Answer 14

Yeah but you are showing different methods

Answer 15

then you integrate .. you should have a list/table of antiderivatives if anything. e^x is a very basic and simple one

Answer 16

so what is the antiderivative of that?

Answer 17

onlys method is working fine :)

Answer 18

if you dont know the antiderivative of e^x by now then you will have to review your material.

Answer 19

Can you finish though

Answer 20

no, i will not do all the work for you. that is not the intentions of this site.

Answer 21

you may attempt it, and we can correct as needed tho

Answer 22

Please I know the answer, I just want to see if you get it

Answer 23

The final answer is 2sinh(x)+c I see no possible way in getting that. @amistre64

Answer 24

if thats the 'correct' solution. then they are expecting you to know hyperbolic trig stuff as well

Answer 25

lets step thru it tho:

what does e^x + e^-x integrate into? then we cam work it into the hyper stuff

Answer 26

isn't it the same thing?

Answer 27

but with a -1 outside

Answer 28

the sites lagging on my end so responses are getting jumbled.

if we know the hyperbolic derivatives, then converting the e^x + e^-x into its hyperbolic equivalent would work all the same

Answer 29

We never went into hyper stuff so its fine

Answer 30

Yes but the exam is not expecting me to know that

Answer 31

e^x integrates to e^x

e^-x is from -e^-x yes

so our integration gets us: e^x - e^-x

but then we still need to know how our hyperbolic functions are defined in terms of e

Answer 32

and a +C of course

Answer 33

did you get your solution from the wolf, or from your material?

Answer 34

Its impossible since Rutgers University never thought us in calculus

Answer 35

ty so much