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Math Help - Integration problem

  1. #1
    Senior Member
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    Apr 2010
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    487

    Integration problem

    The Question:

    \int {sec^4\theta \ d\theta}

    My Attempt:

    \int {sec^2\theta \ sec^2\theta \ d\theta}

    \int {sec^2\theta(tan^2\theta + 1) \ d\theta}

    Let u = tan\theta
    du = sec^2\theta \ d\theta

    \int {u^2 + 1 \ du}

    = \frac{1}{3}u^3 + u
    = \frac{1}{3}tan^3\theta + tan\theta

    However, according to Wolfram Alpha the solution is this.

    What am I doing incorrectly? Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Glitch View Post
    The Question:

    \int {sec^4\theta \ d\theta}

    My Attempt:

    \int {sec^2\theta \ sec^2\theta \ d\theta}

    \int {sec^2\theta(tan^2\theta + 1) \ d\theta}

    Let u = tan\theta
    du = sec^2\theta \ d\theta

    \int {u^2 + 1 \ du}

    = \frac{1}{3}u^3 + u
    = \frac{1}{3}tan^3\theta + tan\theta

    However, according to Wolfram Alpha the solution is this.

    What am I doing incorrectly? Thanks.
    Nothing they are the same thing.

    CB
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  3. #3
    Senior Member
    Joined
    Apr 2010
    Posts
    487
    Ahh. Thank you.
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