Solve ∫(x-1)/(x³+x²+x)^(1÷2)dx

Question

use a substitution as t=x+1+1÷x

Answer 1

I have worked on this problem for several days and gotten nowhere, but maybe this will help since you have gotten no answers yet.

if you make the substitution suggested: x²t = x³+x²+x

dt= [(x²-1)/x]dx and the integral becomes ∫ [x/(x+1)] dt/√t which, as far as I can tell is no help...but maybe you will see something that I do not.

Lastly note that the expression under the radical = x(x³ - 1)/(x-1).

None of this has helped me complete the integral...but maybe you can get it with this help.

I apologize that I am not more helpful.

Also if/when you get the answer. I would be grateful if you would share it with me...I am always interested to learn something new! Thanks.