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Math Help - confused-integration problem-URGENT

  1. #1
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    confused-integration problem-URGENT

    \int_0^2 \frac{(x+1)^2}{x^{2}+1} dx

    ok ive got to \int_0^2 1.dx +\int_0^2 \frac{2x.dx}{x^{2}+1} and got really confused what happens to the limits when you use change of variable say  t=x^{2}+1
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  2. #2
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    If you can see that the derivative of  x^2 + 1 is 2x, you don't need to change your limits. However, if you really want to change it, remember that the limits are just values for x. So:

    because
    t = x^2 + 1
    when  x = 0, t = 1
    when x = 2, t = 5
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