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Math Help - trig integration

  1. #1
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    trig integration

    find each of the following integrals:

    \int tan^4 3x dx

     \int sin^3 2x cos^5 2x dx

     \int tan^3 x sec^5 x dx

    thanks : )
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  2. #2
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    Quote Originally Posted by qzno View Post
    find each of the following integrals:

    \int tan^4 3x dx

     \int sin^3 2x cos^5 2x dx

     \int tan^3 x sec^5 x dx

    thanks : )
    \tan^4(u) =
    \tan^2(u) \cdot \tan^2(u) =
    \tan^2(u)[\sec^2(u) - 1] =
    \tan^2(u)\sec^2(u) - \tan^2(u) =
    \tan^2(u)\sec^2(u) - \sec^2(u) + 1

    use substitution to integrate the first term, last two terms are straight-forward.


    \sin^3(u)\cos^5(u) =
    \sin^3(u)[\cos^2(u)]^2 \cos(u) =
    \sin^3(u)[1-\sin^2(u)]^2 \cos(u) =
    [\sin^7(u) - 2\sin^5(u) + \sin^3(u)]\cos(u)

    straight substitution



    \tan^3{x}\sec^5{x} =
    [\tan^2{x}\sec^4{x}]\sec{x}\tan{x} =
    [(sec^2{x}-1)\sec^4{x}]\sec{x}\tan{x} =
    [sec^6{x} - \sec^4{x}]\sec{x}\tan{x}

    straight substitution
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  3. #3
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    thank you : )
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