Evaluation of integral



Try:

 (%i1) load(abs_integrate)$
 (%i2) load(hyperint)$
 (%i3) extra_integration_methods : 
cons('hyper_int,extra_integration_methods)$

 (%i4) integrate(1/((x-1)^(6/5)*(x+3)^(4/5)),x);
 (%o4) -(5*((x-1)/4+1)^(1/5))/(4^(4/5)*(x-1)^(1/5))

Check:

 (%i5) ratsimp(diff(%,x));
 (%o5) 1/((x-1)^(6/5)*(x+3)^(4/5))

Another example:
 
 (%i6) integrate((x-1)^(6/5)*(x+3)^(4/5),x);
 (%o6) 
(5*4^(4/5)*hypergeometric([-4/5,11/5],[16/5],-(x-1)/4)*(1-x)^2*(x-1)^(1/5))/11

The functionality of hyperint is undocumented, and the function isn't well 
tested
(the hyperint code is in share/contrib).

--bw

maxima-bounces at math.utexas.edu wrote on 03/09/2010 05:04:53 PM:

> [image removed] 
> 
> [Maxima] Evaluation of integral
> 
> Shailesh Ashok Shirali 
> 
> to:
> 
> maxima
> 
> 03/09/2010 05:09 PM
> 
> Sent by:
> 
> maxima-bounces at math.utexas.edu
> 
> Hi,
> I work with Maxima version 5.18.1, front end: wxMaxima 0.8.2.
> 
> I find that Maxima handles with great ease extremely tedious and messy 
> integrals like integrate(sqrt(tan(x)),x) and integrate(tan(x)^(1/3),x).
> 
> But I find that it stumbles on this integral:
> integrate(1/((x-1)^(6/5)*(x+3)^(4/5)),x)
> though the answer is a fairly easy one:
> -(5/4) *(x + 3)^(1/5)/(x - 1)^(1/5).
> 
> Any suggestions on how I could get Maxima to evaluate it? Is there some 
> package to be loaded?
> 
> Thanks!
> 
> Shailesh _______________________________________________
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