How do you evaluate the integral #int x/(root3(x^2-1))#?

1 Answer
Apr 13, 2017

The integral equals #3/4(x^2 - 1)^(2/3) + C#

Explanation:

We will use u-substitution for this integral. Let #u = x^2 - 1#.

Then #du = 2xdx# and #dx= (du)/(2x)#. Call the integral #I#.

#I = int x/root(3)(u) * (du)/(2x)#

#I = 1/2 int 1/root(3)(u)#

#I = 1/2int u^(-1/3)#

#I = 1/2(3/2u^(2/3)) +C#

#I = 3/4u^(2/3) + C#

#I = 3/4(x^2 - 1)^(2/3) + C#

Hopefully this helps!