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Which of the following integrals cannot be evaluated using a simple substitution?

I think it is A because if you would substitute there would be nothing left in the equation? Is that right?

Options
∫√(x-1)
∫1/√(1-x^2)
∫x/√(1-x^2)
∫√(x^2-1)

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12 answers
  1. A.
    let y = x-1
    dy = dx

    ∫√(x-1) = ∫y^.5 dy
    that works

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  2. Wait so A is right or is it wrong?

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  3. B.
    let y = 1 - x^2
    dy = -2 x dx

    ∫1/√(1-x^2) dx = ∫y^-.5 dy/(-2x)
    very awkward

    Hey be sure to include the dx in your integrals

    C will be easy because the x in -2xdx cancels

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  4. You are wrong. A CAN easily be solved
    Be sure to include the dx in your integrals so you include it when you substitute

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  5. Okay will do. So I'm presuming your saying the answer is B. I think D works.

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  6. ∫√(x^2-1) dx <---- NOTE that dx

    let y = x^2-1
    then dy = 2 x dx so dx = dy/2x

    ∫√(x^2-1) DX =∫y^.5 dy/2x

    a mess again

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  7. I had trouble with B and D

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  8. the problem with B and D is that
    dx = dy/f(x)
    so the substitution does not get rid of the x

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  9. In C, that nasty x cancels

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  10. Okay Thanks. That one confused me.

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  11. Im think im going to go with B then

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  12. B and D

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