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Math Help - Integrate

  1. #1
    Junior Member
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    Post Integrate

    Hello everyone while I was studying integrals i came across with a question I could not think how to act. Here it is \int(\cos(\ln(x))dx How to solve this step by step? Thanks
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  2. #2
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    Substitute x = e^u and then use integration by parts.
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  3. #3
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    I am not very familiar with integrating (high school student) and this is a multiple choice(you can take the derivative of the answers) question how can I integrate partially?
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  4. #4
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    Integration by parts

    Integration by parts is the reverse of the product rule. Consider \int x e^x dx. To integrate by parts we need to follow the form: \int u dv = uv - \int v du. So let u=x and dv = e^x dx. Integrating u and differentiating dv gets us du=dx and v=e^x. So now plug in the parts, thus making \int x e^x dx = x e^x - \int e^x dx with the answer being e^x (x-1).

    Follow the substitution Maddas suggested, and integrate!
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  5. #5
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    I have integrated and found the solution but do I wonder if I have to substitute lnx with u by instict what if it was an another function? Thanks for your help BTW
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