integral of sinh(p*ln(x/xsub0))dx

1 answer

using a rather than x0 for ease of typing,

∫sinh(p ln(x/a)) dx

recall that sinh(u) = (e^u - e^-u)/2
so, since
e^(p ln(x/a)) = (e^(ln(x/a)))^p = (x/a)^p
and, since e^-u = 1/e^u,
e^(-p ln(x/a)) = (a/x)^p

sinh(p ln(x/a)) = 1/2 (x^p/a^p - a^p/x^p)

integrate that to get

1/2 (x^(p+1)/((p+1)(a^p)) + a^p/(p-1)x^(p-1)))

(p-1)x^(2p+1) + (p+1)xa^(2p)
--------------------------------------
2(p^2-1) a^p x^p

you can play around with that if you want. If you get really ambitious, you might even end up with

letting u = p*ln(x/a),

x(p cosh(u) - sinh(u))/(p^2-1)
Similar Questions
    1. answers icon 1 answer
    1. answers icon 1 answer
    1. answers icon 0 answers
  1. 1.)Find dy/dx when y= Ln (sinh 2x)my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y
    1. answers icon 2 answers
more similar questions