Integration by Parts

In this video, I showed how and when to use the Integration by Parts technique for integration.
Watch the other video here:

[MartinZimba-suuf]

I regret coming to know about you so late, ,you are excellent professor, , The way you teach is no much to many, ,

[aloixasinclaire]

What would make this even better, is children in the background asking questions about the process while you're going through it! :) Or saying "I finally get it!!!"

[punditgi]

I love 💘 this channel! An awesome teacher. 😃👍

[jan-willemreens]

...Good day Newton, I hope you're still going strong. For the integral of sin(x)cos(x)dx one could also use the well-known trigonometric identity of sin(2x)=2sin(x)cos(x) --> sin(x)cos(x)=0.5sin(2x), and thus solve the integral of 0.5sin(2x)dx instead. For me, this is what makes mathematics so much fun, namely to look for as many possible solution strategies; just like you always say at the end of a presentation, keep learning to stay alive! Thank you for another inspiring presentation... Take good care, Jan-W p.s. L I A T E, remember?

[nadwala_mumala]

Here is me wondering if you're American or Nigerian 😂😂.
Great vids sir. I am a new member just figured you out today. I'm sticking to you ❤😊

[holyshit]

In integration by parts we have to choose parts
u = f(x) and dv=g(x)dx
We choose parts in such way that Integral of vdu is easier to calculate
When integrating dv=g(x)dx we can put any constant we want and sometimes it will be better to use other constant than zero
because this other constant may allow us to do some cancellations
offtopic
I will try to parametrize your t-shirt equation
to easier calculate area enclosed by curve or length
Length of this curve probably would not be expressed with finite number of elementary functions
and operations like additions, multiplications
Let x=cos(t)
y-cos(t)^(2/3)=sin(t)
So your curve should be
x(t)=cos(t)
y(t)=sin(t)+cos(t)^(2/3)
t in [-pi, pi]
Why programs like Wolfram draw only half of this curve although on interval (-pi..-pi/2) or (pi/2, pi)
x(t) = cos(t) is negative (they draw only non negative values for x(t))
but parametrized equation may simplify integration
Ok programs like Wolfam have problems with taking roots of negative numbers
Parametrization i gave should be ok

[printerprinter]

man, i wish u are my lecturer, hell mine is terrifying, the lesson is boring, his voice is so little that even though i am sitting the 1st row, i still barely heard his voice

[bruhnish]

POV: you went to desmos to graph the function on his shirt