- #1

Hepth

Gold Member

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## Main Question or Discussion Point

I have an integration to perform

[tex]\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)[/tex]

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

E1 is the variable. m is the minimum. mB/2 the max.

The integrand is valid over that region, and the two limits are both the points where the integrand crosses the axis.

I'd like an algebraic solution if possible. I can always go to numerical integration, but I'd prefer not to at this stage.

Mathematica won't solve it without limits, it just spits out the integral again. Same thing with the limits, but takes about 5 minutes to spit out the input.

Anyone have any non-numerical ideas?

the plot:

[tex]\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)[/tex]

Code:

```
Sqrt[E1^2 - m^2]
log((m^2 - mB (Sqrt[E1^2 - m^2] + E1))/(
mB (Sqrt[E1^2 - m^2] - E1) + m^2))
```

E1 is the variable. m is the minimum. mB/2 the max.

The integrand is valid over that region, and the two limits are both the points where the integrand crosses the axis.

I'd like an algebraic solution if possible. I can always go to numerical integration, but I'd prefer not to at this stage.

Mathematica won't solve it without limits, it just spits out the integral again. Same thing with the limits, but takes about 5 minutes to spit out the input.

Anyone have any non-numerical ideas?

the plot:

Code:

```
tmp2 = Sqrt[E1^2 - m^2]
Log[(m^2 - mB (Sqrt[E1^2 - m^2] + E1))/(
mB (Sqrt[E1^2 - m^2] - E1) + m^2)];
tmp3 = tmp2 /. {mB -> 5000., m -> 100., \[Lambda]2 -> 1.} //
FullSimplify;
Plot[tmp3, {E1, 100, 6000}, PlotRange -> {{0, 3000}, {0, 40000}}]
```

Last edited: