I have an Integral that is convergent over the range (-inf, Lambda) where 0< Lambda < 1.(adsbygoogle = window.adsbygoogle || []).push({});

I need to change variables to move this to (0.1, 0.9) in such a way that I do not introduce any poor behavior, such as asymptotes or discontinuities as it needs to be well behaved.

Is there a standard practice for this, like when mapping to unit cube/square?

The integral is like :

## \int_{-\infty}^{\Lambda} e^{3 x} (\Lambda - x)^3 P[x] dx ##

where P[x] is some generic polynomial or unknown smooth function.

Thanks for your help!

-Hepth

EDIT :

I guess I can just use something like

## \Lambda + \frac{(t-\text{tp})}{t-\text{tm}}##

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# Integration : Mapping Smoothly (-inf, 2] to [0.1,0.9]

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