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Math Help - Integration

  1. #1
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    Question Integration

    Stuck on trying to integrate

    (4 + 3sec(2x))^2
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  2. #2
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    If we expand it out, we get:

    \int\left[16+24sec(2x)+9sec^{2}(2x)\right]dx

    Now, integrate term by term and it ain't bad.
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  3. #3
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    Quote Originally Posted by galactus View Post
    If we expand it out, we get:

    \int\left[16+24sec(2x)+9sec^{2}(2x)\right]dx

    Now, integrate term by term and it ain't bad.
    Problem is I don't know the integral of 24sec(2x) I know sec^2(x) becomes tan(x). Thats where I was getting stuck, I put the full equation out so that I could check if I had expanded correctly.
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  4. #4
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    Quote Originally Posted by Beard View Post
    Problem is I don't know the integral of 24sec(2x) I know sec^2(x) becomes tan(x). Thats where I was getting stuck, I put the full equation out so that I could check if I had expanded correctly.
    The integral of the secant of x is a tricky one that is hard to see if you don't know it. Consider \sec(x) * \frac{\sec(x)+\tan(x)}{\sec(x)+\tan(x)} and make a u-substitution. Hint:the answer contains a natural log.
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