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Hi. I wanted to know how does one know when to use the substitution rule for integrals and when not too?

Mathematics
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take the derivative of u....if that du is present in the integrand you can use sub
don't use them on saturday night. go out and party

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Other answers:

wait...we're talking about u-sub right? not algebraic sub?
lol sat
@lgbasallote yep I am. I wanted to know when you look at an integral problem, how do you know to use either u-substitution or not.
go out and integrate?
@malexander it involves mastery of derivatives...if you know many derivativves you can see them immediately...if not..you can try u-ing then derive it...
a function multiplied by something that is either the derivative, or a constant multiple of the derivative
\[\int\sqrt{x^3+3}x^2dx\] for example, because the derivative of \(x^3+3\) is \(3x^2\) and what i wrote above was wrong
should have been \[\int f(g(x))g'(x)dx\]
^integral of the chain rule
just noticed lo
lol*
Don't use it on Sundays either, yolo.
Your confusing me @satellite73. Um. Lets say you have these four integrals (question 2). In this question, which one would you need u-substitution and why?
2c
2b
Why those @lgbasallote ?
\[\large \int \frac{3x^3}{\sqrt{x^4 + 1}} = 3\int \frac{x^3}{\sqrt{x^4 + 1}}\] if i let u = x^4 + 1 du = 4x^3 the constant 4 is not important...but x^3 is...and it is present in the integrand so you can use u-sub
2d is u-subbable too
Oh okay. That makes a bit more sense @lgbasallote . However, I thought we were not able to integrate fractions? (Im a cal 1 student, maybe inter grating fractions is in cal 2)
integrating fractions....for example 1/u^2 1/u^2 = u^(-2) according to basic algebra according to basic integration...you can use power rule on that..i assume you're familiar with that note: NEVER use power rule on 1/u <---the integral of that is automatically ln u
also note that i am using u...this is because u is a function of x meaning it is an expression..not limited to only a variable
right, i remember that @lgbasallote about 1/u^2..and also thats fine, we use "u" in class
@lgbasallote ln is in calc 2, so i hope i get to do that next semester hehe...i think i just need to do more problems with integration then...
i see...so you're just learning u-sub...try integrating the ones i said..2b and 2d
will do!
thanks again @lgbasallote ....i have another question...do u mind me asking it here, or posting another question box?
new post...im too lagged for a long thread lol
LOL! ok sounds good

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