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Math Help - u substitution problem

  1. #1
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    u substitution problem

    can someone solve

    ∫tan(x)sec^4(x)dx
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by cummings15 View Post
    can someone solve

    ∫tan(x)sec^4(x)dx

    Consider this

    \int \tan(x)\sec^4(x)\, dx = \int \frac{\sin(x)}{\cos(x)}\cdot\frac{1}{\cos^4(x)}\, dx=-\int \frac{1}{\cos^5(x)}\cdot (-\sin(x))\,dx

    Now substitute z := \cos(x), thus dz= -\sin(x)dx, which gives you

    =-\int\frac{1}{z^5}\, dz=\ldots
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  3. #3
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    so would it equal

    sec^4(x)/4 + C
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  4. #4
    Super Member Failure's Avatar
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    Quote Originally Posted by cummings15 View Post
    so would it equal

    sec^4(x)/4 + C
    Yes, you can also check it on Wolfram's "Integrator": Wolfram Mathematica Online Integrator
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  5. #5
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    thanks
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