need help with this integral

G is gravitational constant
M is mass
a is the distance between the 2 masses

t= integral(dx/sqrt(2GM((1/a)-(1/x)))dx

I'm solving for time in a long physics problem and I'm missing this integral
 
gmarrero3 said:
int(dx/sqrt(2GM(1/a-1/x))dx
Click to expand...

\(\displaystyle \int\frac{dx}{\sqrt{2GM\left (\frac{1}{a}-\frac{1}{x}\right )}}\)

Is this your integral?

If not then try to explain again.

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
but there the dx is part of equation even before i did the integration, so that equation is missing the dx that comes with the integration that why i put the the second dx
 
gmarrero3 said:
but there the dx is part of equation even before i did the integration, so that equation is missing the dx that comes with the integration that why i put the the second dx
Click to expand...

Then there is something wrong with your formulation.

The integral I proposed can be solved with substitution
 
dt= dx/sqrt(2GM(1/a-1/x))

i had this then I did the integral on both sides,
int(dt)dt = int(dx/sqrt(2GM(1/a-1/x)) )dx
t = int(dx/sqrt(2GM(1/a-1/x)) )dx

perhaps I am wrong, if I am, please solve the equation you proposed
 
gmarrero3 said:
dt= dx/sqrt(2GM(1/a-1/x))

i had this then I did the integral on both sides,
int(dt)dt = int(dx/sqrt(2GM(1/a-1/x)) )dx
t = int(dx/sqrt(2GM(1/a-1/x)) )dx

perhaps I am wrong, if I am, please solve the equation you proposed
Click to expand...

Why did you add dt to the left of your equation when it was already there? Why did you add dx to the right of your equation when it was already there? You have already been told a method to solve the integral in a previous reply.
 
t= 1/sqrt(2GM) Int( dx/ sqrt(1/a-1/x)

"1/sqrt(2GM)" I took this out as they are all constant

I think that if I did the substitution correctly I got the answer to t,

t= ((2sqrt(1/a-1/x)/ (sqrt(2GM)) + c

t= 0 x=a

c= 0

t= (2sqrt(1/a-1/x))/ (sqrt(2GM)
 
gmarrero3 said:
t= 1/sqrt(2GM) Int( dx/ sqrt(1/a-1/x)

"1/sqrt(2GM)" I took this out as they are all constant

I think that if I did the substitution correctly I got the answer to t,

t= ((2sqrt(1/a-1/x)/ (sqrt(2GM)) + c

t= 0 x=a

c= 0

t= (2sqrt(1/a-1/x))/ (sqrt(2GM)
Click to expand...

First, is your question about a definite or an indefinite integral? In the latter case, the c cannot be removed. In the former case, it automatically subtracts out and can be ignored.

Second, yes, the integration can be simplified by taking {1 / [(2 * G * M)^(1/2)]} outside the integration.

Third, if x = a, then [(1 / a) - (1 / x)] = 0, right? And dividing by zero is frowned upon in certain circles, no?

Fourth, do you know the trick of replacing x with u and dx with du to simplify the integral? An obvious first choice would be to try substituting
u = [(1 / a) - (1 / x)] and making the appropriate conversion of dx to du.
 
gmarrero3 said:
dt= dx/sqrt(2GM(1/a-1/x))

i had this then I did the integral on both sides,
int(dt)dt = int(dx/sqrt(2GM(1/a-1/x)) )dx
t = int(dx/sqrt(2GM(1/a-1/x)) )dx

perhaps I am wrong, if I am, please solve the equation you proposed
Click to expand...

Substitute:

\(\displaystyle \frac{1}{x} \ = \ \frac{1}{a}\cdot sin^2(\theta)\)

the resulting function (as a function of ?) after integration is pretty daunting. I solved it using Wlfram-alfa (free web).
 
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