A Nasty integral -

**WalkingInMud** · April 22nd 2008, 12:20 PM

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,

**colby2152** · April 22nd 2008, 12:26 PM

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?

**mr fantastic** · April 22nd 2008, 07:16 PM

Originally Posted by colby2152

[snip]Now, what can we do about that?

A leading question ....?

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