How to do this integration?

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shaq

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Tw and σ^2 are constants.
 

The indefinite integral evaluates to
(π/2)^½ × σ × erf(x / (√2 × σ))

(sorry about these symbols)

Depending on x and Tw, you'll need either a good, or a better approximation to erf.

(i.e. (π/2)^½ × σ × (erf((x + Tw) / (√2 × σ)) - erf(x / (√2 × σ)))

Added after 11 minutes:

This might get you started on that last part ...
https://mathworld.wolfram.com/Erf.html

Search the web for approximations, and check your problem against values from tables to see if the accuracy's sufficient.
 


Dear LouisSheffield,

What does the "n" mean?
 

It was trying to be a "pi"
Also, the square root applies only to the 2.

Added after 3 minutes:

I used MathCAD to do the integration.
Depending on definition, the wolfram site eludes to there being two competing definitions for erf(), depending on normalization.

When you get close (i.e. a routine for erf), give me a PM or an email, and we can figure out if your routine is normalized the same way as MathCAD's.

(I would hate for your answers to be off by a constant factor)
 

[color=darkred[b]](1/√(x^4+x^2+1)[[/[/b]color]quote="shaq"]Tw and σ^2 are constants.[/quote]∫
 

this integral could not be expressed by an elementary equation, could it?
 

Nope - only an approximation can, but the goodness of the approximation has to take many factors into account:
1) The value of x,
2) The value of Tw, and
3) The required precision of the approximation.

A form of this equation Q(x) is used often in calculating bit-error-rates. An approximation with an additive error of < 1% will hardly do for BERs on the order of 10^-16.
 

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