Question

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

Answer 1

@satellite73

Answer 2

take the derivative of u....if that du is present in the integrand you can use sub

Answer 3

don't use them on saturday night. go out and party

Answer 4

wait...we're talking about u-sub right? not algebraic sub?

Answer 5

lol sat

Answer 6

@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.

Answer 7

go out and integrate?

Answer 8

@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...

Answer 9

a function multiplied by something that is either the derivative, or a constant multiple of the derivative

Answer 10

\[\int\sqrt{x^3+3}x^2dx\] for example, because the derivative of \(x^3+3\) is \(3x^2\) and what i wrote above was wrong

Answer 11

should have been
\[\int f(g(x))g'(x)dx\]

Answer 12

^integral of the chain rule

Answer 13

just noticed lo

Answer 14

lol*

Answer 15

Don't use it on Sundays either, yolo.

Answer 16

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?

Answer 17

2c

Answer 18

2b

Answer 19

Why those @lgbasallote ?

Answer 20

\[\large \int \frac{3x^3}{\sqrt{x^4 + 1}} = 3\int \frac{x^3}{\sqrt{x^4 + 1}}\] 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

Answer 21

2d is u-subbable too

Answer 22

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)

Answer 23

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

Answer 24

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

Answer 25

right, i remember that @lgbasallote about 1/u^2..and also thats fine, we use "u" in class

Answer 26

@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...

Answer 27

i see...so you're just learning u-sub...try integrating the ones i said..2b and 2d

Answer 28

will do!

Answer 29

thanks again @lgbasallote ....i have another question...do u mind me asking it here, or posting another question box?

Answer 30

new post...im too lagged for a long thread lol

Answer 31

LOL! ok sounds good