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Math Help - [SOLVED] Simple integration problem

  1. #1
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    [SOLVED] Simple integration problem

    \int sec(3x) tan(3x) dx

    It's an easy problem, yet... I don't know how to go about solving it. Can anyone shed some light?
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  2. #2
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    Here is a hint: \sec x\tan x is the derivative of something.

    Hope this helps!
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  3. #3
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    Right, sec 3x tan 3x becomes sec 3x.

    What confuses me is what's to be done after that.




    =

    \int sec(3x)dx

    Do I use the substitution rule?
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  4. #4
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    Let u=3x\mbox{ Then }du=3dx. Then upon substitution you get.

     \frac{1}{3}\int sec(u)tan(u)\,du

    Go from there.
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  5. #5
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    How can I proceed? Do I use the general power rule?

    I end up with sec 3x^2/6 + C which apparently is not the answer.
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  6. #6
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    go through your inventory of the derivatives of the trig functions. such as \frac{d}{dx}sec(x)
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  7. #7
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    Could you please be a little bit more specific? is sec x tan x ... how does that help me? I already did that step. My final answer is wrong though.
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  8. #8
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    If the derivative of sec(x) is sec(x)tan(x), then what is the integral of sec(x)tan(x)?
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  9. #9
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    sec x.

    But I already did that part. Why are you bringing it up?
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  10. #10
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    by substitutin u in you get sec(u) as there is 1/3 outside in the integral the final answer comes to 1/3*sec(3x)
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  11. #11
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    well, you have \frac{1}{3}\int sec(u)tan(u)\,du, so after you integrate that, and substitute 3x back in for u, what do you think?
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  12. #12
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    Quote Originally Posted by Fermatwannabe View Post
    by substitutin u in you get sec(u) as there is 1/3 outside in the integral the final answer comes to 1/3*sec(3x)
    Thank you
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  13. #13
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    Well that is the answer to the original integral you posted. Can you double check it? Unless your answer is \frac{1}{cos(3x)}+C
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  14. #14
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    Quote Originally Posted by Archduke01 View Post
    Thank you
    is it 1/cos(3x) if not then im stumped
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  15. #15
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    Quote Originally Posted by Archduke01 View Post
    \int sec(3x) tan(3x) dx

    It's an easy problem, yet... I don't know how to go about solving it. Can anyone shed some light?
    You are trying to find the antiderivative of \sec{3x}\tan{3x}

    The derivative of sec{3x} is 3\sec{3x}\tan{3x}

    So the antiderivative of 3\sec{3x}\tan{3x} is sec{3x}+C

    Then what would be the antiderivative of \sec{3x}\tan{3x}?
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