# 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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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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