Question

integral problem involving e^x

Answer 1

\[\int\limits \frac{ 3 }{ 5e^x -2 }dx \]

Answer 2

i tried multiplying the top and bottom by the conjugate but that didnt seem to help and i also tried adding and subtracting 5e^x to the top but that trick didn't really help either

Answer 3

try substitution u=5E^x-2

Answer 4

but that leaves a 1/5e^x

Answer 5

correct...u take care of that by integrate by parts then

Answer 6

hmmm so (3/5e^x)(1/u) would be the problem that i need to take care of by integration by parts?

Answer 7

couldn't i simplify that to like 3/(u^2 +2u)?

Answer 8

\[5e^x-2=\left( \sqrt{5}e^{\frac{ x }{ 2 }}+\sqrt{2} \right)\left( \sqrt{5}e^{\frac{ x }{ 2 }}-\sqrt{2} \right)\]

Answer 9

@pgpilot326 ty :)

Answer 10

let u be one of the factors

Answer 11

ok so you factored the denominator but how does letting u be one of the factors help?

Answer 12

doesn't really... hold on and let me think a minute...

Answer 13

ans is right here: http://www.wolframalpha.com/input/?i=integrate+3%2F%285e%5Ex-2%29dx

so i think it is just substitution then followed by IBP...gtg...good luck :)

Answer 14

might have to do straight up by parts

Answer 15

ok so if do like @superdavesuper says then i would take 5e^x -2 as u

Answer 16

that would leave me with 3/(5e^xu)

Answer 17

would i start doing integration by parts from there or would i make the 5e^x into (u+2) since 5e^x -2 = u so 5e^x = u + 2

Answer 18

if you let u = 5e^x-2 then du = 5e^x dx =( u+2) dx

Answer 19

multiply numerator and denominator by
\[e ^{-x}\]

Answer 20

then it becomes integral of 3du + 3/u du

Answer 21

3u +3ln|u| +c = 3(5e^x-2)+3ln|5e^x-2| + c

can check if derivative is original integrand

Answer 22

\[I=\int\limits \frac{ 2e ^{-x} }{ 5-2e ^{-x} }dx=?\]

Answer 23

so @surjithayer (3/2)(ln(5-2e^-x)) + C

Answer 24

@surjithayer you put a 2 instead of a 3 on the top

Answer 25

sorry i goofed. @surjithayer has the easiest way.

Answer 26

it's ok but im sure your way is still equivalent though

Answer 27

yes ,it is 3 in the numerator.,thanks for the correction.

Answer 28

not too sure... it get's a bit messy and i don't think it resolves into something integrable

Answer 29

ok well thank you for the help, i still have a lot of tricks and experience to accumulate in math