# Integration help

find

## Homework Equations

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

## The Attempt at a Solution

I honestly don't know what to do?

## Answers and Replies

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

I don't know how to do that?

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

So is that a substitution?

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

dextercioby
Homework Helper
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.

Yes, hyperbolic substitution would work here.

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 ?

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.