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Math Help - Another integration help!

  1. #1
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    Another integration help!

    evaulate the integral by substitution
    37. \int^1_{0} \frac{e^z+1}{e^z+z}*dz
    What substitution should I be making?
    Any tips in general for choosing substitutions?
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  2. #2
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    You need to be able to see an "inner function" and the inner function's derivative as a factor.

    Notice that \displaystyle \frac{d}{dz}(e^z + z) = e^z + 1.

    So what do you think you will use as your substitution?
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  3. #3
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    \displaystyle u=e^z+z=e^z+1
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    \displaystyle u=e^z+z=e^z+1
    \displaystyle e^z + z is NOT always equal \displaystyle e^z + 1...
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  5. #5
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    I meant to put \displaystyle du=e^z+1
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  6. #6
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    Thanks! I missed that e^z' = e^z
    For some reason I thought I would have to use the chain rule for that.
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  7. #7
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    Quote Originally Posted by dwsmith View Post
    \displaystyle u=e^z+z=e^z+1
    I hope what you meant to post is \displaystyle u=e^z+z \Rightarrow du = e^z+1.
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