# Thread: How do I solve integral tanh(7x)?

1. ## How do I solve integral tanh(7x)?

I have a long integral and broken it up and solved everything besides $\displaystyle \int tanh 7x dx$

2. Originally Posted by circuscircus
I have a long integral and broken it up and solved everything besides $\displaystyle \int tan 7x dx$
a simple substitution of $\displaystyle t = 7x$ will do

3. Originally Posted by Jhevon
a simple substitution of $\displaystyle t = 7x$ will do
Yea understood but the problem is my book gives the integrals for only sinh, cosh,sech^2,csc^2,sech, and csch but not tanh nor coth

4. Originally Posted by circuscircus
Yea understood but the problem is my book gives the integrals for only sinh, cosh,sech^2,csc^2,sech, and csch but not tanh nor coth
oh, you changed the question.

note that $\displaystyle \tanh x = \frac {\sinh x}{\cosh x}$

and it is still an easy substitution problem

5. $\displaystyle Dx tanh 7x$

$\displaystyle = Dx \frac{sinh(7x)}{cosh(7x)}$

use quotient rule
$\displaystyle = \frac{7cosh(7x)cos(7x) - 7sinh(7x)sinh(7x)}{cosh(7x)^2}$

so is it like this?

6. Originally Posted by circuscircus
$\displaystyle Dx tanh 7x$

$\displaystyle = Dx \frac{sinh(7x)}{cosh(7x)}$

use quotient rule
$\displaystyle = \frac{7cosh(7x)cos(7x) - 7sinh(7x)sinh(7x)}{cosh(7x)^2}$

so is it like this?
......are you confused about something? or did you type the wrong question originally? you should be finding the integral, not taking the derivative

7. OH man sorry I was out of it

Yea, how would I solve the integral of e^x-e^-x / e^x+e^-x

8. Originally Posted by circuscircus
OH man sorry I was out of it

Yea, how would I solve the integral of e^x-e^-x / e^x+e^-x
there is no need to write the formulas that way. just use the substitution $\displaystyle u = \cosh x$

9. u = coshx
du = sinhx

1/u du

ln |u| + C

ln |coshx|+c

Thanks!

10. Originally Posted by circuscircus
u = coshx
du = sinhx

1/u du

ln |u| + C

ln |coshx|+c

Thanks!
not quite. remember, we are dealing with $\displaystyle \tanh {\color {red}7}x$

but i think you have the idea