Integration - When to Use U-substitution or Integration by Parts

[@laman8914]

Normally, when there is a function, which is a product of 2 other functions, Integration by Parts will most of the time be the more suitable solution method. Here we have a function that is indeed the product of 2 functions and Integration by parts is used appropriately. As rule of thumb, choose that function of which the derivative is easier to find.

[@muhsinaislam5946]

What do u mean by "product of 2other function"?

[@Twilight_Tasogare608]

@@muhsinaislam5946in this case, the two functions are x^3 (a polynomial) and ln 2x (natural log). Other examples of functions include: rational functions, square root cube root, trig functions (sin , cos)

[@tabishtabi3528]

Is there any this type of thing for integration by substitution

[@sathyasayesh9914]

The shortcut to decide which is U, you can use the acronym LPET, where L-logarithm, P-Polynomial, E-exponential, T-Trigonometry. It goes in the order of priority of L PET, where you chose Logarithm,Poly.....in that order for your choice of U. Indians can remember it as lal pet, which roughly translates to "beloved/darling" pet

[@alfedrale6660]

Ty for sharing this with us!

[@Polarzz]

I've used the acronym LIATE for integration by parts. Logarithmic, Inverse Trig, Algebraic, Trig, Exponential

[@rzsteez3970]

@@Polarzz I use the same thing except its ILATE, no idea how both of the methods work if the L and I and switched around 💀

[@user-ju1kk3vx5v]

For polys, is it strictly only (1+x)^n or can it have other functions inside of it like sinx, cosx, lnx and other stuff? Such as (2cosx + 42)^5

[@adamishensem1235]

Very much thanks Sir.

[@emilyfoss305]

Nice vid. Love how clean your work is. Male math teachers often struggle with penmanship haha

[@moodymonstrosity1423]

Ive heard that when there are trignometric functions with a power are involved, we have to do the integration by parts twice or thrice, if its true please do a tutorial on those...

[@Twilight_Tasogare608]

Check out the DI method of integration by parts. It handles multiple integration by parts nicely. Black pen red pen (bprp) has a nice video explaining it

[@Jayson223ad]

"Teachers and textbooks are kinda in love with factoring" this made me laugh, so true. Are there problems you can use both techniques on?

[@staycalm9979]

Excellent explanation. Your strategies makes it easier to decide what to use when.

[@rul1175]

Finally someone that explains it.

[@MarwanAlarnous]

Thaaaaank you. I truly needed that!

[@elliottmason5330]

very good video. thank you for that. excellent explanation

[@xanderxander3132]

Very well explained !!!!! U got a sub ....very intuitive, keep up the good work very nice talent of yours!!!

[@captain_cloudd]

was "u got a sub" an intentional joke?

[@kataraarts3027]

@@captain_cloudd LOL best joke on the internet

[@EmilyPrewett]

I have a test in 30 minutes thanks for this

[@crazyjester993]

thank you mam you are awesome but please do for ordinary differentail equation

[@tanapoomohmwattanavijitkul7052]

THANK YOU SO MUCHHHH

[@Tj2k01]

Great video by the way

[@jaimeesmith501]

at 7:28 is the minus sign in the wrong position? in the formula the minus sign is right before the integration sign. so just curious. it is kind of confusing.

[@Twilight_Tasogare608]

X^4/4 is the integral of x^3. The integral is evaluated, so the integral sign goes away

[@Tj2k01]

how would you recognise a deriviative pair

[@MathHop]

Anytime an integral has two expressions, and one of the expressions is the derivative of the other - you have a derivative pair. For example: if you had the integral of -15x^4(-3x^5-1)^12 dx you wold use u-sub because the derivative of -3x^5-1 is -15x^4.

[@Tj2k01]

@@MathHop Could do an example when the question is 4x(1+x)^3 would you use u sub or parts

[@MathHop]

Use parts for that one, here is a video of it kzbin.info/www/bejne/iYu2lnemrbaMirM

[@williamessel2958]

Love the name of the channel. Typical😂😂

[@LtCzr]

meg

[@Tj2k01]

What about intergration of 24x(x^2-5)^5

[@MathHop]

That one is u-sub Here you go: kzbin.info/www/bejne/fJ7CY6hodqicZqc

[@prestondavison45]

Mila Kunis