In my book I have a proof for this integral: = = =
How can I simplify = into ?
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You could actually perform the substitution, rather than carrying it in the notation where it seems to be confusing you.
Do you really mean "proof"? Maybe just a demonstration? The last marvelous step to the natural logarithm is a bit magic.
Originally Posted by Bart In my book I have a proof for this integral: = = =
How can I simplify = into ? That sucks!!! the way it's carried out there.
This is a prime candidate for tan subsitution.
We arrive at
And simplify to
Noting that for all x, so we can disregard the absolute value
I don't totally hate what it was trying to do. With a little more experience in the sightly unusual notation, it isn't quite terrible.
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