Asked by Henry

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)
Answered by Damon
A.
let y = x-1
dy = dx

∫√(x-1) = ∫y^.5 dy
that works
Answered by Henry
Wait so A is right or is it wrong?
Answered by Damon
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
Answered by Damon
You are wrong. A CAN easily be solved
Be sure to include the dx in your integrals so you include it when you substitute
Answered by Henry
Okay will do. So I'm presuming your saying the answer is B. I think D works.
Answered by Damon
∫√(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
Answered by Damon
I had trouble with B and D
Answered by Damon
the problem with B and D is that
dx = dy/f(x)
so the substitution does not get rid of the x
Answered by Damon
In C, that nasty x cancels
Answered by Henry
Okay Thanks. That one confused me.
Answered by Henry
Im think im going to go with B then
Answered by Damon
B and D
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