## malexander 3 years ago Hi. I wanted to know how does one know when to use the substitution rule for integrals and when not too?

1. saifoo.khan

@satellite73

2. lgbasallote

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

3. satellite73

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

4. lgbasallote

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

5. lgbasallote

lol sat

6. malexander

@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.

7. lgbasallote

go out and integrate?

8. lgbasallote

@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...

9. satellite73

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

10. satellite73

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

11. satellite73

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

12. lgbasallote

^integral of the chain rule

13. lgbasallote

just noticed lo

14. lgbasallote

lol*

15. marcoduuuh

Don't use it on Sundays either, yolo.

16. malexander

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?

17. lgbasallote

2c

18. lgbasallote

2b

19. malexander

Why those @lgbasallote ?

20. 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

21. lgbasallote

2d is u-subbable too

22. malexander

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)

23. lgbasallote

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

24. lgbasallote

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

25. malexander

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

26. malexander

@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...

27. lgbasallote

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

28. malexander

will do!

29. malexander

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

30. lgbasallote

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

31. malexander

LOL! ok sounds good