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I need help on this indefinite integral

  1. Jul 20, 2007 #1
    1. The problem statement, all variables and given/known data
    ok im given this problem

    indef. int (1+tan^2*5x)dx i need to use the u subsitution method to find the answer but i cannot seem to find what to subsitute

    the worksheet says the answer is " one-fifth*tan5x+C


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 20, 2007 #2

    Gib Z

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    Homework Helper

    The using the Pythagorean Identity [tex] 1+ \tan^2 x = \sec^2 x[/tex], we can change your problem to:
    [tex]\int \sec^2 (5x) dx[/tex]. then let u= 5x. du= 5 dx, or dx = (1/5) du.

    We can take constants out of the integral, so it becomes [tex]\frac{1}{5} \int \sec^2 u du[/tex]. You should know that the derivative of tan x is sec^2 x, so the integral is [tex]\frac{1}{5} \tan u + C = \frac{1}{5} \tan (5x) + C[/tex]
     
  4. Jul 21, 2007 #3
    thanks for the help, i got the trig idenity, but the problem was that i was letting u=sec^25x
     
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