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Math Help - integration of x.secx.tanx

  1. #1
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    integration of x.secx.tanx

    how would you integrate x.secx.tanx dx??
    thanks for any help
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  2. #2
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    \int x\sec{x}\tan{x}~dx = \int x(\sec{x})'~dx = x\sec{x} - \int \sec{x}~dx

    It can be easily shown that \int \sec{x}~dx = \ln|\sec{x}+\tan{x}| by multiplying the integral expression with \frac{\sec{x}+\tan{x}}{\sec{x}+\tan{x}}
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  3. #3
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    tanx

    what happened to the tanx???
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  4. #4
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    Recall that:

    \frac{d}{dx} \sec{x}= (\sec{x})' = \sec{x}\tan{x}

    I wrote \sec{x}\tan{x} in an equivalent form (\sec{x})' as it is easier and faster to see what u and v when using integration by parts.
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  5. #5
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    \int x\cdot sec(x)tan(x)dx

    Use parts, Let u=x, \;\ dv=sec(x)tan(x)dx, \;\ du=dx, \;\ v=sec(x)

    We get:

    xsec(x)-\int sec(x)dx

    Now, it's easier, huh?.
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  6. #6
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    thanks

    thanks to both of you i was having trouble seeing that one
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