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March 22nd, 2015, 04:18 AM   #1
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how reliable are online integration calculators

As I'm studying alone, I sometimes need online tools to check my calculations. But I noticed some inconsistency with online integration calculators. For the expression -15/(2x-450) I got different answers from two different calculators.

Integral Calculator: Wolfram Mathematica Online Integrator
-15/2*ln(450-2x) from Wolfram

Online Integral Calculator • Find Integrals and Antiderivatives!
-15/2*ln(2x-450) from this one

Did I read something wrong, or are they giving me different results?

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March 22nd, 2015, 06:01 AM   #2
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Actually, they're both correct ... and both incorrect. Should be ...

$\displaystyle \int -\frac{15}{2x-450} \, dx = -\frac{15}{2}\ln|2x-450| +C$

The one you accept as correct depends if $2x-450 >0$ or if $450-2x>0$.

That is why absolute value of the log argument is necessary if you don't know which of the above is true.

Note $|2x-450|=|450-2x|$ takes care of either situation.
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March 22nd, 2015, 06:08 AM   #3
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Also, check out the result my TI CAS gives ...
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March 22nd, 2015, 06:24 AM   #4
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Sorry I'm still rather a beginner at calculus, how does it get to x-225?

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March 22nd, 2015, 04:25 PM   #5
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Quote:
Originally Posted by czakal View Post
... how does it get to x-225?
$\displaystyle \ln|2x-450| + C_1$

$\displaystyle \ln(2|x-225|) + C_1$

$\displaystyle \ln(2) + \ln|x-225| + C_1$

since $\ln(2)$ is just a constant ...

$\displaystyle \ln|x-225| + C_2$
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