How to integrate fraction?

How do you integrate

1/(100+t) dt

1 Answer

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  • 1 decade ago
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    Use the substitution method.

    The original function is:

    1/(100 + t) dt

    let u = 100 + t

    then differentiate u:

    du/dt = 1

    du = dt

    From these information, you can reword the function again into:

    1/u du

    Now, you'll need to remember a formula where the integral of 1/x = ln |x|

    This applies here, where you can integrate this function into:

    ln |u| + C

    But u = 100 + t,

    so the answer will equal to:

    ln |100 + t| + C --> finished.

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