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Math Help - Integrating (x + 1) using substitution

  1. #1
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    Integrating (x + 1) using substitution

    Hey forum how would I go about in order to compute this indefinite integral,

    \int \, (x^2 +1)^2 \, \text{d}x \ ?

    I can't seem to eliminate all x-variables using u = x^2 + 1. I know I can simply compute it by expanding the integrand but I want to do it using substitution in particular.
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  2. #2
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    Re: Integrating (x + 1) using substitution

    Nevermind, my answer only works for 1 over your problem
    Last edited by jeduhi; July 29th 2012 at 09:49 AM.
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  3. #3
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    Re: Integrating (x + 1) using substitution

    Quote Originally Posted by SweatingBear View Post
    Hey forum how would I go about in order to compute this indefinite integral,

    \int \, (x^2 +1)^2 \, \text{d}x \ ?

    I can't seem to eliminate all x-variables using u = x^2 + 1. I know I can simply compute it by expanding the integrand but I want to do it using substitution in particular.
    You can't do this using substitution. Expand the integrand instead.
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    Re: Integrating (x + 1) using substitution

    Quote Originally Posted by Prove It View Post
    You can't do this using substitution.
    How come?
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    Re: Integrating (x + 1) using substitution

    Quote Originally Posted by MathCrusader View Post
    How come?
    I'll rephrase that. You can't perform a u substitution, because doing so requires the substituted function's derivative being a factor of your integrand. If you let u = x^2 + 1, then you need to have a factor of 2x in your integrand as well. You don't, so you can't use u substitution.

    You could possibly use a trigonometric or hyperbolic substitution, but doing so is time consuming and pointless, when a perfect square is quick and easy to expand and the resulting integrand easy to integrate using the power rule.
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