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Math Help - Integration question

  1. #1
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    Integration question

    Hi have the following integral, i have expanded the numerator, and then thinking a change of variable on the denominator but doesnt seem to be working heres, the question:
    Evaluate the following integral
    (x+1)^2dx/x^2+1 Between the limits of 2 and 0.

    Many thanks in advance.

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  2. #2
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    hello dear
    try to expand (x+1)^2 and see what u can do
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  3. #3
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    Quote Originally Posted by islam View Post
    hello dear
    try to expand (x+1)^2 and see what u can do
    I expanded that and couldnt see anything obvious there :/
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  4. #4
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    \displaystyle \int{\frac{(x + 1)^2}{x^2 + 1}\,dx} = \int{\frac{x^2 + 1 + 2x}{x^2 + 1}\,dx}

    \displaystyle = \int{1 + \frac{2x}{x^2 + 1}\,dx}.

    Now use an appropriate substitution.
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  5. #5
    Super Member Quacky's Avatar
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    Quote Originally Posted by Prove It View Post
    \displaystyle = \int{1 + \frac{2x}{x^2 + 1}\,dx}.
    Now use an appropriate substitution.
    Substitution isn't required in every situation, Prove It! This is simply a case of \displaystyle\int\frac{f'(x)}{f(x)} dx=ln|f(x)|+c, unless I'm mistaken. Obviously, there's the 1 to deal with, but that isn't too difficult to integrate.
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  6. #6
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    the problem is that the OP is currently learning these things and how fast and easy one can detect a simple integral requires practice.

    we can't force to OPs to immediately learn what we consider trivial for us.
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  7. #7
    Super Member Quacky's Avatar
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    That doesn't mean, though, that we should always blindly resort to substitution. If a method is present, and the OP is taught to ignore it, how will he expect to progress? If he doesn't understand my method, he doesn't have to use my method, but that doesn't mean that the method isn't important and should be completely ignored.
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  8. #8
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    ah, but i was justifying Prove's post, in a sense, i was explaying why he didn't suggest another method.
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  9. #9
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    Quote Originally Posted by Quacky View Post
    Substitution isn't required in every situation, Prove It! This is simply a case of \displaystyle\int\frac{f'(x)}{f(x)} dx=ln|f(x)|+c, unless I'm mistaken. Obviously, there's the 1 to deal with, but that isn't too difficult to integrate.
    Which is, of course, a rule that comes from substitution.

    For deep understanding, a student needs to find this rule for him/herself.
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  10. #10
    Super Member Quacky's Avatar
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    Quote Originally Posted by Prove It View Post
    Which is, of course, a rule that comes from substitution.

    For deep understanding, a student needs to find this rule for him/herself.
    I am disinclined to agree. If he substitutes, I think it's highly unlikely that he will discover this rule. I think that it is similarly unlikely that he will then go on to remember this rule for the permanent future. I think that if he has been taught the derivation of this rule himself in class, then being able to apply it is sufficient - if he substitutes, his substitution will develop, but he will not attempt to spot such shortcuts in the future. However, this is irrelivent: I merely suggested a much faster and more efficient method, it's up to the OP whether or not he uses it depending upon his knowledge of integration.
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  11. #11
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    problem has been solved and there's no much to do here.

    you talk about that in other forums.
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