MHB Unraveling the Mystery: How WolframAlpha Got from Step 1 to 2

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The discussion focuses on the confusion surrounding the transition from step 1 to step 2 in a WolframAlpha calculation. Participants express uncertainty about the appearance of an extra factor of two and the proper factoring of variables in the integral. One contributor suggests that multiplying the outside by two and the inside by one-half could explain the discrepancy, but acknowledges that it doesn't fully resolve the issue with the missing term. Another participant reflects on the challenges of late-night calculus practice, indicating a desire for a simpler method, while also appreciating the learning experience. The conversation highlights the complexities involved in understanding calculus transformations.
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How did WolframAlpha get from step 1 to 2?

I don't get where that extra "two" came from (outside of the integral), and I don't get how there is an extra u factored out.

My initial thought was maybe they mutlipled the outside by two, and inside by 1/2 so that equals 1, but it still doesn't account for the missing 1/sqrt(x) to complete "du".
 

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$ du = \frac{1}{2 \sqrt{x}}dx $

We get $ 2 \sqrt{x} \ du = dx $

2u \ du = dx

Now substitute and pull out the constant 2 ...

:D
 
How did I miss that the first time :( The ramifications of doing calculus up all night for fun.
Thanks!
 
A simpler approach would be to expand .
 
ZaidAlyafey said:
A simpler approach would be to expand .

Very true, but I wanted to practice without it :) Thanks guys!
 
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