# Tough Integral (Log)

Gold Member
I posted this in the mathematical/computation software forum but maybe theres an algebraic trick I don't know to help me solve this.

I need to compute an integral of:
$$\sqrt{\text{E1}^2-m^2} Log\left( \frac{m^2-m_B E1-m_B\sqrt{E1^2-m^2}}{m^2-m_B E1+m_B \sqrt{E1^2-m^2}}\right)$$

over the region {E1,m,mB/2}

the limits of integration are well defined in the equation, though the function is asymptotic near the upper bound. But it still has a value there.

I can't seem to integrate this. Mathematica just spits the input back out. I know its possible because I can numerically integrate it for what I want and it gives a reasonable answer. Unfortunately I REALLY want an algebraic solution...

Does anyone have any ideas? An integral of a sqrt times a log of a function of the variable. I've tried some substitution methods, nothing seems to simplify.

Thanks for the help!

EDIT:I think I got something by letting U= Log[everything], it can be algebraic, but its sooo long... any other choices?

Last edited:

Redbelly98
Staff Emeritus
Homework Helper
I posted this in the mathematical/computation software forum but maybe theres an algebraic trick I don't know to help me solve this.

I need to compute an integral of:
$$\sqrt{\text{E1}^2-m^2} Log\left( \frac{m^2-m_B E1-m_B\sqrt{E1^2-m^2}}{m^2-m_B E1+m_B \sqrt{E1^2-m^2}}\right)$$

over the region {E1,m,mB/2}
What is the variable here? Why are there three integration limits {E1,m,mB/2} instead of two?

Gold Member
variable is E1. From m to mB/2

I used mathematicas way of saying that sorry.

EDIT:I think I got something by letting U= Log[everything], it can be algebraic, but its sooo long... any other choices?

Well, you can also use Mathematica do perform these steps and simplify the end result...

Ben Niehoff