[DTube] How to Integrate ln(x)

masterwu (59)in #steemstem • 6 years ago (edited)

I'm in the process of uploading all of my Youtube videos to DTube, where they can be recorded on the Steem blockchain.

In this video I demonstrate how to find the integral or antiderivative of the natural log of x, ln(x), using integration by parts.

Integration by parts is written as...

∫udv = uv - ∫vdu

You may be wondering, there's only one part to this integral: ln(x). Well, we can make the 'u' part be ln(x) and the 'dv' part be equal to dx.

Thus...

du = (1/x)dx
v = x

Please watch the video for the full tutorial.

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6 years ago in #steemstem by masterwu (59)

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branbello (49) 6 years ago

Do you have any videos on differential equations and trig substitution? I have a bit to teach myself before classes next fall and videos would be a huge help with that.

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masterwu (59) 6 years ago (edited)

Yes and yes.

I have a series on differential equations here: this is the latest post, might be a little advanced, but at the bottom, there's a list of tutorials at the bottom that goes from the beginning.
I have yet to transfer all of my YouTubes to DTube yet, but you'll find a playlist of integration tutorials with some that use trig substitution here: https://www.youtube.com/playlist?list=PL0YzbD4vPtxK3b8LJ8zZRd0W4kohoj0Jm