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Math Help - Integration with substition

  1. #1
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    Integration with substition

    Integrate



    They gave me the U for this integral but im not sure how im suppose to work it into the problem. Can someone show me the steps to do this?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by NickytheNine View Post
    Integrate



    They gave me the U for this integral but im not sure how im suppose to work it into the problem. Can someone show me the steps to do this?
    it's a substitution problem, and they gave you the substitution, just follow the method. what are you supposed to do next? find du ...
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by NickytheNine View Post
    Integrate



    They gave me the U for this integral but im not sure how im suppose to work it into the problem. Can someone show me the steps to do this?
    \int\frac{\sec^2\left(\frac{1}{x^{39}}\right)}{x^{  40}}dx

    If we let z=\frac{1}{x^{39}} then dz=\frac{-1}{x^{40}}. So

    \int\frac{\sec^2\left(\frac{1}{x^{39}}\right)}{x^{  40}}dx\overbrace{\mapsto}^{z=\frac{1}{x^{39}}}-\int\sec^2(z)dz
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  4. #4
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    so the final answer would be -tan(1/(x^39)) + C
    is this correct?
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  5. #5
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    Yes.
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