Interesting integral with square and cube roots: ∫dx/(√x+∛x)

Evaluating the indefinite integral of 1/(√x+∛x) with respect to x, using a substitution and polynomial long division.
A more general version of this integral is here: • A more general integra...
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#calculus #integration #mathematics #maths #math #education #integral #substitution #exponent #power #indefiniteintegral #root #squareroot #sqrt #cuberoot #polynomial #longdivision #logarithm #lcm #lowestcommonmultiple

[@paulcaira]

Brilliant work, and so clearly presented.

[@DrBenYelverton]

Thanks - I was taught well!

[@SayanTheStreamer]

Thanks :) really helped me... ❤

[@DrBenYelverton]

Glad to hear that!

[@hvcreations4170]

Good explanation

[@btsmochimi7924]

Pls do more videos like this...its really good❤

[@DrBenYelverton]

Thanks! Maybe take a look at my integration playlist, there are some other unusual integrals in there: kzbin.info/aero/PLTntRzhyShSHdvJbAB2fIbP1ul-jMDvIM&si=nCKTieL2dj_NcnRO

[@TheoremeDeSarkowski]

Good job👍👍

[@anushkanegi56]

Thank u sir you explain very good 😁😁

[@gnumani]

Mui bien senor Ben

[@AliSiddiqui55]

What mic do you use?

[@DrBenYelverton]

It's a Samson Q2U (my earlier videos were recorded using a Blue Yeti, which picked up a lot more background noise).

[@AliSiddiqui55]

I see. It’s very good.

[@DrBenYelverton]

@@AliSiddiqui55 Yup, I'm pleased with it!