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

[Dethrone]

View attachment 1242

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".

 

[agentredlum]

From

$ 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

 

[Dethrone]

How did I miss that the first time :( The ramifications of doing calculus up all night for fun.
Thanks!

 

[alyafey22]

A simpler approach would be to expand .

 

[Dethrone]

A simpler approach would be to expand .

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