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Homework Help: Anti differentiation using U sub help

  1. Apr 3, 2010 #1
    I am self studying for my AP Calc exam. I have just started on integration and I need a few pointers for a few questions. So here it is....

    y= (e^x)/(1+(e^x)^2)

    So I set u=e^x
    du=e^x

    then I am stuck.

    the second question is (btw [{( are all used as parentheses to make it abit less confusing)

    y=(x^2)/[{(x^3)+1)}^12]
    I setted u=(x^3)+1
    du=3x^2
    (1/3)du = (x^2)dx
    (1/3)integral sign [1/(u^12)]du
    stuck there after

    and 3

    y=[(lnx)^3]/x

    do i set x as u? or lnx?

    Last of all I have no clue on number 4 which is

    y=sin(2x)*e^[cos(2x)]

    Many thanks!
     
  2. jcsd
  3. Apr 3, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Try u= 1+ (e^x)^2

    1/u^12= u^(-12). Integrate that.

    It should be obvious that "u= x" does not help- it just replaces the letter x with the letter u! So try u= ln x.

    Try u= cos(2x).
     
  4. Apr 3, 2010 #3
    Bump up
     
  5. Apr 4, 2010 #4
    Finished with all of them...unsure about number 1. Ended up with arctan*e^x +c
     
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