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Integral question

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral:
    the integral of 9r4^r dr

    2. Relevant equations

    integral of f(x)g'(x)dx = f(x)g(x) - integral of f'(x)g(x)dx

    integral of udv = uv - integral vdu

    u = f(x), dv = g'(x) dx

    3. The attempt at a solution

    I first started by pull the 9 out to the front:
    9 integral of r4^r dr
    I then set u=r, du=dr, dv=4^r, v=(4^r)/ln(4)
    I used the formula: integral of udv = uv - integral vdu
    and got: the integral of 9r4^r dr = [(r4^r)/ln4] - the inegral of (4^r)/ln4 dr
    I then pulled the 1/ln4 out of the last part and got:
    the integral of 9r4^r dr = [(r4^r)/ln4] - 1/ln4[the inegral of 4^r dr]

    I was also able to get the anti-derivative of the [the inegral of 4^r dr] as (1/ln(4)) 4^r
    I got stuck here, i don't know how to put all of it back together, help please?
  2. jcsd
  3. Jan 27, 2010 #2


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    You did all the hard stuff already, though you forgot to multiply the 9 through.

    This is what you said you have so far:

    [tex]\int 9r4^rdr=9\left(\frac{r4^r}{\log 4}-\frac{4^r}{(\log 4)^2}\right)[/tex]

    Aren't you done except for tacking on +C to the end?
  4. Jan 27, 2010 #3
    yes, but does it needs to be simplified? how do you do that?
    my assignment is online and it keeps on telling me that i'm getting the wrong answer.
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