How Do You Integrate ∫(1/sqrt(1-(2/x)-((x^2)/3)))dx?

  • Thread starter Thread starter Nilupa
  • Start date Start date
  • Tags Tags
    Functions
Nilupa
Messages
18
Reaction score
0
Please help me to find this integral.

∫(1/sqrt(1-(2/x)-((x^2)/3)))dx
 
Physics news on Phys.org
Hey Nilupa and welcome to the forums.

Try multiplying the integral by x/x and factor out the denominators with x in it (i.e. get rid of the 2/x term and make all terms in the square root positive powers of x).
 
chiro said:
Hey Nilupa and welcome to the forums.

Try multiplying the integral by x/x and factor out the denominators with x in it (i.e. get rid of the 2/x term and make all terms in the square root positive powers of x).

Thank you,, I did that. but,it is still impossible...
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Volume between a region (above x-axis and below parabola) and a surface
Replies
4
Views
2K
Calculating radius of gyration of plane figure about x-axis
Replies
5
Views
2K
Prove that the integral is equal to ##\pi^2/8##
3
Replies
105
Views
4K
Verify Green's Theorem in the given problem
Replies
10
Views
2K
How to Integrate [1/(x^2 + 3)] dx?
Replies
5
Views
3K
How To Integrate 1/[sqrt (x^2 + 3x + 2)] dx?
Replies
44
Views
5K
A question about definite integrals and series limits
Replies
12
Views
2K
How should I show that the transformation makes the system Hamiltonian?
Replies
4
Views
2K
Integrals that keep me up at night
Replies
22
Views
3K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top