# A Nasty integral -

• Apr 22nd 2008, 01:20 PM
WalkingInMud
A Nasty integral -
Any Ideas on how to Approach this one? ...

$\int\sqrt{[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}}du$

We have a $sech(u)$ and its derivative $-tanh(u)sech(u)$ and this suggests some sort of substitution maybe, but the radical makes it a bit nasty for Me.

Any Ideas? ...Thanks Heaps,
• Apr 22nd 2008, 01:26 PM
colby2152
Quote:

Originally Posted by WalkingInMud
Any Ideas on how to Approach this one? ...

$\int\sqrt{[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}}du$

We have a $sech(u)$ and its derivative $-tanh(u)sech(u)$ and this suggests some sort of substitution maybe, but the radical makes it a bit nasty for Me.

Any Ideas? ...Thanks Heaps,

Thinking out loud here, but simplify the radical...

$[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}$

$1-2sech(u)+sech^2(u)+tanh^2(u)sech^2(u)$

Use trig substitution: $tanh^2(u)=sech^2(u)-1$

$1-2sech(u)+sech^2(u)+[sech^2(u)-1]sech^2(u)$

$1-2sech(u)+sech^2(u)+sech^4(u)-sech^2(u)$

$1-2sech(u)+sech^4(u)$

Now, what can we do about that?
• Apr 22nd 2008, 08:16 PM
mr fantastic
Quote:

Originally Posted by colby2152
[snip]Now, what can we do about that?