Integration: Help With Log SQRT 1+x^2

[XtremePhysX]

Homework Statement

find

Homework Equations

$$\int log\sqrt{1+x^2}dx$$

The Attempt at a Solution

I honestly don't know what to do?

 

[dextercioby]

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

 

[XtremePhysX]

I don't know how to do that?

 

[dextercioby]

$$x = \sinh t$$ would be the obvious candidate.

 

[XtremePhysX]

So is that a substitution?

 

[XtremePhysX]

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

 

[dextercioby]

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]

Yes, hyperbolic substitution would work here.

 

[XtremePhysX]

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]

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.