- #1

DryRun

Gold Member

- 838

- 4

**Homework Statement**

Integral of sech^3 (x)

**The attempt at a solution**

sech^3 (x) = (sech x)(sech^2 (x)) = (sech x)(1-tanh^2 (x))

And then i expanded by multiplying:

(sech x)(1-tanh^2 (x)) = (sech x) - (sech x)(tanh^2 (x))

The integral of sech x can be found.

But what about the integral of (sech x)(tanh^2 (x))?

I've tried various substitutions, but failed. Let t = tanh x and also let t = sech x.

I also tried this way:

(sech x)(tanh^2 (x)) = (sech x)(1 - sech^2 (x)) = sech x - sech^3 (x)

But then i end up with the original problem again.