- #1

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dx/((a-x)^(1/2)*(b-c(x-d)^3/2)). I've tried finding the integral of this with non-trig substitution methods but cannot solve it. Any help would be appreciated.

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- Thread starter MegaFlyman
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- #1

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dx/((a-x)^(1/2)*(b-c(x-d)^3/2)). I've tried finding the integral of this with non-trig substitution methods but cannot solve it. Any help would be appreciated.

- #2

eumyang

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I don't see an equation here. (Where's the equals sign?) Start by writing the original problem and show us what work you have.I've separated the variables of this differential equation and end up with

dx/((a-x)^(1/2)*(b-c(x-d)^3/2)).

- #3

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dx/dy = b(a-x)^1/2 - c(a-x)^1/2 * (x-d)^3/2

Separating variables results in my original posted equation

dy = dx/((a-x)^1/2 * (b-c(x-d)^3/2))

I have tried the substitution, u = (a-x)^1/2, x = a-u^2, dx = -2udu. Which results in

dy = -2dx/(b-c((-u^2+a)-d)^3/2)

Any further non-trig substitutions does not help to simplify. I believe a trig substitution is required but I have little experience with trig subs. I have already put any many hours looking for a solution and would like to know if a trig sub could be used to solve this. Thanks

- #4

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- #5

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I'm not seeing anywhere to go after that either. But thanks for the input.

- #6

Ray Vickson

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I'm not seeing anywhere to go after that either. But thanks for the input.

The integral is VERY complicated. It involves a lengthy formula that uses the roots of a 6th degree polynomial whose coefficients are functions of a, b, c and d. I did the integral in Maple, but if you do not have access to Maple you could try to submit it to Mathematica. Wolfram Alpha failed to find the integral.

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