MX2 Integration Marathon (1 Viewer)

YonOra

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Show all necessary working, please. V tricky.
 

notme123

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Same adding and subtracting the same thing trick as the previous question:









IBP on the first integral gives:



Second integral is just reverse chain rule

So in total:
this method is more intuitive and quicker I reckon esp if you know what the integral of inverse tan is off by heart.
 

idkkdi

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This was the intended method.
legit where did i go wrong, hella confused its probably one of the subs.

or is this a possible alternate form? desmos ain't registering it for some reason tho
 

vernburn

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legit where did i go wrong, hella confused its probably one of the subs.

or is this a possible alternate form? desmos ain't registering it for some reason tho
Ngl I can’t even follow your solution
 

idkkdi

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legit where did i go wrong, hella confused its probably one of the subs.

or is this a possible alternate form? desmos ain't registering it for some reason tho
desmos not looking right, what happened in my subs bruh
 

Qeru

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Really cool integral from stanford which a lot of people have probably seen before:

 

idkkdi

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let x = tan u
x/ sec^2u / x^2 === > tan^3 u ===> tanusec^2u - tanu let tan u = z, z^2/2 + ln |cos u| lowkey messed it up, say where plz
botched the algebra.

but basically my way.
you sub in x = tan u.
u get ucot^2 u.
and by parts it.
this works right? @vernburn
 

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