Can someone me with a quick integral?

[MaximumTaco]

I don't know how to do fancy symbols, but

Integral of 1/((sinh[x])^2) .dx

I got as far as 1/2 Int(sech(2x)). d(2x), is this the right approach?

Thanks .

 

[Muzza]

Your approach might work, but it seems to me like the integral could be easily handled by rewriting the hyperbolic sine in exponential form and then doing a substitution (or partial fractions (but that seems rather messy)).

 

[mathwonk]

this is probably easy if you remember the basic trig integrals and their analogies with hyperbolic trig integrals. i.e. remember the derivative of tan is sec^2, and sec = 1/cos.

also the derivative of cot is -csc^2 and csc = 1/sin.

Hence by analogy, we should try cosh/sinh as the antiderivative of 1/sinh. does it work?

 

[JonF]

It write it in it’s exponent form then break it into two fractions and take each integral separately.