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Another Trigonometric Integral Problem Help Me

  1. Aug 23, 2008 #1
    1. The problem statement, all variables and given/known data
    ∫sec^2 (x) * tan (x) dx


    2. Relevant equations
    sec^2 (x)= 1+tan^2(x)


    3. The attempt at a solution
    =∫(1+tan^2 (x) or tan (x) tan (x)) tan (x) dx u=tan x, du=sec^2 dx

    ∫ (1+u^2) u du

    = ∫u+u^2)du
    = u^2/2 + u^3/3 = 1/2 tan^2(x)+ 1/3 tan^3 (x) +c

    the answer in the back of the book is 1/2 tan^2(x)+c

    what did i do wrong
     
  2. jcsd
  3. Aug 23, 2008 #2

    rock.freak667

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    Homework Helper

    You didn't need to use this identity: sec2 (x)= 1+tan2(x)

    u=tan x, du=sec^2 dx <-- This is an ideal start

    [tex]\int tan(x) (sec^2(x) dx)[/tex]



    Do you see where to replace your tan(x) as u and so on now?
     
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