Intergrating hyperbolics

[ed2288]

Hi, can anyone tell me how to integrate (coshx)^2?
thanks

[nightmare]

write it as the integral of cosh(x).cosh(x).
Integrating this by parts gives
cosh(x).sinh(x) - S sinh(x)^2 dx, where S=integral sign.

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

take the integral of cosh(x)^2 over to the LHS and integrate the 1 t o get x, then divide everything by 2 and you will have
S cosh(x)^2 dx = (cosh(x)sinh(x) + x) / 2

QED

[Peter Pedant]

blimey well done nightmare

just in passinng does this extend by induction to

S (coshx)^n.dx ? using the usual notation

thanks

PP

[nightmare]

To PP
the expression becomes hideously complicated