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Math Help - Integration by parts

  1. #1
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    Integration by parts

    can someone show the steps to these 2 questions please

    integrate (5x^3)/(x^2 +9) dx

    integrate x/(x+1) dx
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  2. #2
    o_O
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    #1. Long divide to get: 5\int \frac{x^3}{x^2 + 9} = 5\int \left(x - \frac{9x}{x^2 + 9} \right) \ dx

    Use u = x^2 + 9 for that second term.

    #2. Add '0' and separate the fractions: \int \frac{x {\ \color{red}+1 - 1}}{x+1} \ dx \ = \ \ \int \left( 1 - \frac{1}{x+1}\right) \ dx

    (Or use partial fraction decomposition if you're not comfortable with adding the '0')

    No integration by parts here!
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