## malexander Group Title Hi. I wanted to know how does one know when to use the substitution rule for integrals and when not too? 2 years ago 2 years ago

1. saifoo.khan Group Title

@satellite73

2. lgbasallote Group Title

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

3. satellite73 Group Title

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

4. lgbasallote Group Title

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

5. lgbasallote Group Title

lol sat

6. malexander Group Title

@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 Group Title

go out and integrate?

8. lgbasallote Group Title

@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 Group Title

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

10. satellite73 Group Title

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

11. satellite73 Group Title

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

12. lgbasallote Group Title

^integral of the chain rule

13. lgbasallote Group Title

just noticed lo

14. lgbasallote Group Title

lol*

15. marcoduuuh Group Title

Don't use it on Sundays either, yolo.

16. malexander Group Title

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 Group Title

2c

18. lgbasallote Group Title

2b

19. malexander Group Title

Why those @lgbasallote ?

20. lgbasallote Group Title

$\large \int \frac{3x^3}{\sqrt{x^4 + 1}} = 3\int \frac{x^3}{\sqrt{x^4 + 1}}$ 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 Group Title

2d is u-subbable too

22. malexander Group Title

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 Group Title

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 Group Title

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 Group Title

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

26. malexander Group Title

@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 Group Title

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

28. malexander Group Title

will do!

29. malexander Group Title

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

30. lgbasallote Group Title

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

31. malexander Group Title

LOL! ok sounds good