Question

integrate coshx/(3sinx-2coshx)
thank you in advance

Answer 1

have u tried this urself yet?

Answer 2

and is that sin suppose to be sin or sinh?

Answer 3

yup, by definition, but im redoing it right now

Answer 4

sorry sinh not sin

Answer 5

this is a long integral

Answer 6

i didnt get the answer, my final answer is \[\int\limits cotxdx\] which is wrong.

Answer 7

yes it is, ok bear with me i ll go step by step

Answer 8

let me know if u dont understand any step

Answer 9

1.multiply numerator by denominator by -sech^3(x)\[\int\limits_{}^{} -\frac{ sech^2(x) }{ 2sech^2(x)-3sech^2(x)\tanh(x) }dx\]

Answer 10

wait why -sech^3 x?

Answer 11

it will make your integral less painful

Answer 12

after this u can use u= tan(x) substitution

Answer 13

how did u do ur first step?

Answer 14

from my original answer?

Answer 15

yes

Answer 16

i used it definition

Answer 17

oh using definition will take too long

Answer 18

just a question, where did sinh and cosh go?

Answer 19

didnt u read my 1. step multiply num and denom by -sech^3(x)

Answer 20

sorry a mistake in my calculation

Answer 21

so should i go further with next step

Answer 22

\[x+\frac{ 3 }{ 5 } \ln(\left| (e^{2x}-5)e^{-2x} \right|)+c\]

Answer 23

by definition this should be ur answer^

Answer 24

unfortunately it's not.. i

Answer 25

i think i mess up in the middle but i already erased it, so i cant show you

Answer 26

do u have to do it by definition, have u learnt substitution yet?

Answer 27

yeah i have learnt subs but im not sure which one should be subs

Answer 28

now continue after tanhx=u, the denom sech^2 x is change to 1-tanh^2 x?

Answer 29

u want me to continue?

Answer 30

sure

Answer 31

2.let u=tanh(x) and sub this into eq. Remember sech^2(x)=1-tanh^2(x)\[\int\limits_{}^{}-\frac{ sech^2(x) }{ (3\tanh(x)-2)(\tanh^2(x)-1) }dx\]

Answer 32

3.sub u=tanh(x) and du=sech^2(x)dx
\[\int\limits_{}^{}-\frac{ 1 }{ (3u-2)(u^2-1) }du\]

Answer 33

factor out constants in this case is -1
and use partial fraction \[-\int\limits_{}^{}(\frac{ 1 }{ 10(u+1)}-\frac{ 9 }{ 5(3u-2)}+\frac{ 1 }{ 2(u-1) })du\]

Answer 34

r u getting it?

Answer 35

wait, why the denom relationship change, i mean how can it became from ()-() to ()()

Answer 36

i used partial fraction

Answer 37

ohhh... ok i get it

Answer 38

read the top part i am writing , i am also explaining what i did in that step

Answer 39

then next, just integrate then subs the u, right?

Answer 40

yes

Answer 41

ok thank you, n sorry im a slow learner

Answer 42

its ok :)