1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluate using any method Number 2

  1. Aug 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate using any method:

    [tex]\int\frac{8x^3+10} {\sqrt[3]{5x-4}}[/tex]dx

    2. Relevant equations

    3. The attempt at a solution

    I'm lost on this one.
    Last edited: Aug 2, 2010
  2. jcsd
  3. Aug 2, 2010 #2


    User Avatar
    Science Advisor

    Since it is that cube root in the denominator that is causing the trouble, a kind of obvious substitution is [itex]u= 5x- 4[/itex]. Then du= 5dx or dx= (1/5)du.

    Also, 5x= u+ 4 so x= (u+ 4)/5. Replacing x by that in [itex]8x^3+ 10[/itex] gives you a cubic, in u, in the numerator divided by [itex]\sqrt[3]{u}= u^{1/3}[/itex]. That reduces to a sum of terms involving [itex]u^{3- 1/3}= u^{8/3}[/itex], [itex]u^{2- 1/3}= u^{5/3}[/itex], and [itex]u^{1- 1/3}= u^{-2/3}[/itex].
  4. Aug 2, 2010 #3
    Where do you get the 5x=u+4?
  5. Aug 2, 2010 #4


    Staff: Mentor

    From the substitution u = 5x - 4.
  6. Aug 2, 2010 #5
    So do you get something like:

    8[tex]\int\frac{(u+4/5)^3 + 10}{u^(1/3)}[/tex]

    That's U raised to the 1/3 on the denominator
  7. Aug 2, 2010 #6


    Staff: Mentor

    It's not u + 4/5 in the numerator -- it's (1/5)(u + 4). Also, where is du in your integral? You seem to be ignoring it.
  8. Aug 2, 2010 #7
    Yea thats what I meant. I don't understand where the Du goes.

    8[tex]\int\frac{((u+4)/5)^3 + 10}{u^(1/3)}[/tex]

    So that is right? Then does du takes the spot of the 5?
  9. Aug 2, 2010 #8


    User Avatar
    Homework Helper

    Use u=5x-4 then du=5dx, insert this into the integral to obtain:
    \int\frac{8x^3+10} {\sqrt[3]{5x-4}}dx=\frac{1}{5}\int\frac{8((u+4)/5)^{3}+10}{u^{1/3}}du
    Now all you have to do is expand the cube and integrate using
    \int x^{n}dx=\frac{1}{n+1}x^{n+1}+c
  10. Aug 2, 2010 #9
    What is n?
  11. Aug 2, 2010 #10


    User Avatar
    Homework Helper

    [tex]n[/tex] is a number, like 3 or 2/3.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook