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Math Help - Evaluate the integral

  1. #1
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    Evaluate the integral

    Hello,
    please evaluate the integral.Thanks.
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  2. #2
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    Hello, m777!

    It seems to be straight-forward.
    . . Exactly where is your difficulty?


    Evaluate: . \int^4_1\left(\frac{1}{t}\!\cdot\!i + \frac{1}{5-t}\!\cdot\!j + \frac{1}{2t}\!\cdot\!k\right)\,dt

    We have: . \ln(t)\!\cdot\!i - \ln(5-t)\!\cdot\!j + \frac{1}{2}\ln(t)\!\cdot\!k\,\bigg]^4_1

    . . = \;\left[\ln(4)\!\cdot\!i - \ln(1)\!\cdot\!j + \frac{1}{2}\ln(4)\!\cdot\!k\right] - \left[\ln(1)\!\cdot\!i - \ln(4)\!\cdot\!j + \frac{1}{2}\ln(1)\!\cdot\!k\right]

    . . = \;\left[\ln(4)\!\cdot\!i - 0 + \frac{1}{2}\ln(4)\!\cdot\!k\right] - \left[0 - \ln(4)\!\cdot\!j + 0\right]

    . . = \;\ln(4)\!\cdot\!i - \ln(4)\!\cdot\!j + \frac{1}{2}\ln(4)\!\cdot\!k

    . . = \;\frac{1}{2}\ln(4)\!\cdot\!(2i - 2j + k)

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