sarah12345
how do i intergrate cosh^2 x ?
thanks

Here is a solution....I have no idea how it is done.
Use the double angle formula:

cosh(2x) = 2cosh^2 x -1

cosh^2 x = ½(1+cosh 2x)

intergrating gives:

½x + ¼sin2x
sarah12345
how do i intergrate cosh^2 x ?
thanks

cosh 2x = 2cosh²x - 1
½cosh 2x + ½ = cosh²x
Integrate LHS
Get
¼sinh 2x + ½x

Aitch

[As produced earlier by JaF! ]
thanks i get it now!! also if tanh x = 1/2
how would you work out cosh x and sinh x ?

thanks alot
sarah12345
how do i intergrate cosh^2 x ?

thanks

OR
cosh x=e^x+e^(-x)/2
cosh^2x= 1/4[e^(2x)+2+e^(-2x)]
int cosh^2(x)= 1/4[1/2e^(2x)+2x-1/2e(-2x)]+C
=1/4[e^(2x)-e^(-2x)/2]+x/2+C
=1/4sinh(2x)+x/2+C
sarah12345
thanks i get it now!! also if tanh x = 1/2
how would you work out cosh x and sinh x ?

thanks alot

Start from 1 - tanh²x = sech²x...

Aitch
sarah12345
thanks i get it now!! also if tanh x = 1/2
how would you work out cosh x and sinh x ?

thanks alot

tanhx=e^(x)-e^(-x)/e^(x)+e^(-x)=1/2
=> 2[e^(x)-e^(-x)]=e^(x)+e^(-x)
e^(x)-3e^(-x)=0
e^(2x)-3=0
e^(x)=rt(3)
Aitch
Start from 1 - tanh²x = sech²x...

Aitch

...then get cosh²x from sech²x, then sinh²x from cosh²x...

Aitch
sarah12345
thanks i get it now!! also if tanh x = 1/2
how would you work out cosh x and sinh x ?

thanks alot

tanh x = (sinh x) / (cosh x) = 1/2

Hence, sinh[x] = 1 and cosh[x] = 2 by comparing, no?
Peevee
tanh x = (sinh x) / (cosh x) = 1/2

Hence, sinh[x] = 1 and cosh[x] = 2 by comparing, no?

Um... How about sinhx=2 and coshx=4?

Aitch

[In]
Aitch
Um... How about sinhx=2 and coshx=4?

Aitch

[In]

Ahh, u got me there!