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Math Help - Can Somebody please solve this integral for me (showing their steps)??

  1. #1
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    Can Somebody please solve this integral for me (showing their steps)??

    e ^ -x * tan(e^ -x)

    Sorry I would try and explain everything I've tried but i'm on pre-test overload going through tons of problems.

    I thought maybe u would be e to the -x but I couldn't get it to work.

    thanks
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Can Somebody please solve this integral for me (showing their steps)??

    Let
    u = tan(e^-x) and v' = e^-x and try to use integration by parts. [I suggest v' as I do because it's easier to integrate. You might have to use a different method]

    \int u(x) v'(x) \, dx = u(x) v(x) - \int u'(x) v(x) \, dx

    EDIT: You can also use u substitution and let u = e^-x
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  3. #3
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    Re: Can Somebody please solve this integral for me (showing their steps)??

    Hello, skinsdomination09!

    Your game plan was a good one . . . It should have worked.


    \int e^{\text{-}x}\tan(e^{\text{-}x})\,dx

    We have: . \int \tan(e^{\text{-}x})\,(e^{\text{-}x}dx)

    Let u \,=\,e^{\text{-}x} \quad\Rightarrow\quad du \,=\,\text{-}e^{\text{-}x}dx \quad\Rightarrow\quad e^{\text{-}x}dx \,=\,\text{-}du

    Substitute: . \int \tan u (\text{-}du) \;=\;-\int\tan u\,du \;=\;\ln|\cos u| + C

    Back-substitute: . \ln|\cos(e^{\text{-}x})| + C
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