Results for integrate(Rational(1,4)*(1/(4-t)))

[Raphael Timbó]

Hi,

I was trying to use:

integrate(Rational(1,4)*(1/(4-t)))

This was returning:

−14log(4t−16)

I was not expecting this result... I went to sympy gamma to see the steps and I saw that:

Antiderivative forms:

• integrate(1/(4*(-t + 4)), t)
  −14log(4t−16)

But when you check the steps you have:

The answer is:

−14log(−t+4)+constant

I could not understand why the results are different...

Any explanation?

Thank you!

[Raphael Timbó]

Since the images with the results are distorted:

First result:

-(1/4)*log(4*t - 16)

Results given by the step-by=step solution on sympy gamma:

-(1/4)*log(-t + 4)

[Aaron Meurer]

A multiplication of a constant inside a log is the same as adding a constant to the log (log(a*b) = log(a) + log(b)). So both are valid integrals, because of the constant of integration. You can check yourself that both give the original expression if you differentiate them.

Aaron Meurer

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[Kalevi Suominen]

There are several integrators in SymPy. The latter form is produced by ratint.

>>> from sympy.integrals.rationaltools import ratint
>>> from sympy.abc import t
>>> ratint(1/(4*(-t + 4)), t)
-log(t - 4)/4

Kalevi Suominen

[Aaron Meurer]

See https://github.com/sympy/sympy/issues/11017. It would be nice if we could fix ratint to not flip signs in the logarithm. 

Aaron Meurer

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[Aaron Meurer]

With that being said, either answer is wrong if you want a real function. For that, you need log(abs(4 - t)). But unfortunately, the abs() answer isn't valid in the general complex case, which is why SymPy doesn't return it. 

Aaron Meurer

[Raphael Timbó]

Thank you very much!

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