# Having trouble with these!

• Oct 27th 2009, 04:48 AM
dannyshox
Having trouble with these!
1. Show that (coshx + sinhx)[to the power of] n = coshnx + sinhnx

2. Determine the integral of tanhxdx

3. Determine the integral of 4dx/(e to the x + e to the -x)squared

PS How can i use the proper math symbols?!!

Thanks!(Rock)
• Oct 27th 2009, 05:22 AM
tonio
Quote:

Originally Posted by dannyshox
1. Show that (coshx + sinhx)[to the power of] n = coshnx + sinhnx

This is trivial applying the definition of the hyperbolic functions

2. Determine the integral of tanhxdx

$\tanh x=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1}=1-\frac{2}{e^{2x}+1}$.
Take it from here now (if you know integrals of usual trigonometric functions this one won't surprise you).

3. Determine the integral of 4dx/(e to the x + e to the -x)squared

[colo=blue]Get some ideas from the above

Tonio[/color]

PS How can i use the proper math symbols?!!

Using LaTex

Thanks!(Rock)

.
• Oct 27th 2009, 05:45 AM
dannyshox
I dont understand how u got that in 2.! I was looking at other examples and they use substitution?

Also would it be right to use inegrations by parts in 3.?
• Oct 27th 2009, 08:20 AM
tonio
Quote:

Originally Posted by dannyshox
I dont understand how u got that in 2.! I was looking at other examples and they use substitution?

Also would it be right to use inegrations by parts in 3.?

For 2.- Multiply by $\frac{e^x}{e^x}$

For 3.- You can try parts or note that $=\frac{4}{e^x+e^{-x}}=\frac{1}{\cosh^2x}=\sec \!\!h^2x$

Tonio
• Oct 27th 2009, 09:51 AM
dannyshox
thanks(Clapping)