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Math Help - How do I solve this integral using another method such as substitution?

  1. #1
    s3a
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    How do I solve this integral using another method such as substitution?

    I attempted this and got nowhere (see attached work if you want). I then used Wolfram Alpha to see how to do it and that tanh stuff is something I have to see. Of course, I've heard of it from my previous teacher but, I have never actually covered it in a course. Furthermore, my teacher does not expect me to use such a method (I'm assuming), so I was hoping someone could help me figure this out using substitution or something of the sort. (I have not learned integration by parts for instance)

    Wolfram Alpha's "work": http://www.wolframalpha.com/input/?i=integral+4%2F(x^2+-+1)

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Yes there is an easier way - that is, if you're ok with partial fractions. Factorise the denominator...

    \frac{4}{(x - 1)(x + 1)} = \frac{A}{x - 1} + \frac{B}{x + 1}

    ... you just have to figure out A and B. Then you have a direct way to the log version of the integral that Wolfram presents as a re-writing of tanh.
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  3. #3
    s3a
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    I didn't know what partial fractions were or how to do them but after watching a couple youtube videos, I get it. However, I still get the wrong answer but thankfully I get the correct magnitude which must mean that I am on the right track. My work is attached so can you please point out my mistake?
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