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Evaluate the following indefinite integrals.

Can you show all the steps please!

a) ∫xe^x^2+10 dx
b) ∫x-2/x-4 dx

  • Math -

    ∫xe^x^2+10 dx

    the first term fits the pattern perfectly for differentiating terms of the type e^(u)
    notice if I differentiate e^(x^2) , I get
    2x e^(x^2), I am given half of that, so

    ∫xe^x^2+10 dx
    = (1/2) e^(x^2) + 10x + C

    for the second:
    ∫x-2/x-4 dx

    using one step of a long division, we can show that
    (x-2)/(x-4)
    = 1 + 2/(x-4)

    so ∫x-2/x-4 dx
    = ∫1 + 2/x-4 dx
    = x + 2ln(x-4) + C

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