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Math Help - integrals

  1. #1
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    integrals

    Determine the integrals:

    curently studying this module and looking at a few examples.
    if someone could explain when working these out, would help be gratefully in doing other examples: three examples thank you

    3 + 3 dx
    3 3

    ∫cos(4x+7) dx

    ∫ 3xsinx dx

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  2. #2
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    The first one is unreadable...

    For the second, make the substitution \displaystyle u = 4x + 7 \implies du = 4\,dx

    For the third, you need to use integration by parts...
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  3. #3
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    first example has come out wrong it is meant to me Sum of x3 over 3 + 3dx over xcubed
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  4. #4
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    Do you mean \displaystyle \int{\frac{x^3}{3} + \frac{3}{x^3}\,dx}? If so, rewrite it as \displaystyle \int{\frac{1}{3}x^3 + 3x^{-3}\,dx} and go from there...
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  5. #5
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    yep that is correct
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