- #1

- 207

- 10

## Homework Statement

integral of Sech^5(x)*Csch(x) dx

## Homework Equations

I think Coth^2(x)-1 = Csch^2(x) may help

## The Attempt at a Solution

I tried a few things. The latest being breaking the problem up and doing some re-working.

int(Sech^2(x)*Sech^3(x)*Csch(x) dx) I then multiplied the whole expression by Sinh^3(x)/Sinh^3(x) to get

int(Sech^2(x)*tanh^3(x)*Csch^4(x) dx)

I then got rid of the Csch^4 by breaking it up into two (Coth(x)^2-1)'s and multiplying the tanh^3(x) term through to end up with

int(Sech^2(x)*tanh(x)*(coth^2(x)+tanh^2(x) dx)

I think I just made a huge mess and probably some mistakes...

I was doing really well through two books worth of problems until this one :s, one of the very last ones lol.

If I could get some guidance or a little hint to move me toward a better understanding of the technique needed here I'd greatly appreciate it.

Thank you.