Homework Help: Integration help

XtremePhysX · Aug 11, 2012

1. The problem statement, all variables and given/known data

find

2. Relevant equations

[tex]\int log\sqrt{1+x^2}dx[/tex]

3. The attempt at a solution

I honestly don't know what to do?

dextercioby · Aug 11, 2012

I would use a hyperbolic function to make a substitution to get rid of the square root.

XtremePhysX · Aug 11, 2012

I don't know how to do that?

dextercioby · Aug 11, 2012

[tex] x = \sinh t [/tex] would be the obvious candidate.

XtremePhysX · Aug 11, 2012

So is that a substitution?

XtremePhysX · Aug 11, 2012

the answer is xlnx-x+c is that right?

dextercioby · Aug 11, 2012

You'll have to make the calculations on your own. I just gave you a point to start from, assuming you have knowledge of hyperbolic functions. Another option is to use integration by parts.

Millennial · Aug 11, 2012

Yes, hyperbolic substitution would work here.

XtremePhysX · Aug 11, 2012

Millennial said: ↑

Yes, hyperbolic substitution would work here.

Hello mill
but is the answer xlnx-x
also, is the derivative of ln(x^2) just 2/x and the derivative of (lnx)^2 is 2lnx/x ?

Millennial · Aug 11, 2012

Xtreme, why don't you try differentiating your answer to check whether if it is correct?
And answering your question about derivatives: Yes, they are both correct.