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Math Help - Integrate this:

  1. #1
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    Integrate this:

    \int \frac{5x+3}{x^2+8x+25}
    I really dont know how to start this integral
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    \int \frac{5x+3}{x^2+8x+25}
    I really dont know how to start this integral
    Note that \frac {5x + 3 }{x^2 + 8x + 25} = \frac {5x + 20 - 17}{x^2 + 8x + 25} = \frac {5x + 20}{x^2 + 8x + 25} - \frac {17}{x^2 + 8x + 25}

    thus, \int \frac {5x + 3 }{x^2 + 8x + 25}~dx = \int \frac {5x + 20}{x^2 + 8x + 25}~dx - \int \frac {17}{x^2 + 8x + 25}~dx

    for the first integral, use the substitution, u = x^2 + 8x + 25

    for the second, complete the square of the denominator and simplify so you can get it in the form to get the arctan integral, that is, try to get it in the form of c \frac 1{u^2 + 1}, where c is a constant, and u is a function of x. (it is easier than you think, try it)
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