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Integral:

\int_{ 0 }^{ 2 }\left[\;\int_{ x }^{ 2 }\left( x\,\sqrt{y^3+1} \right)\,dy \;\right]\;dx

Variable for outside integration and limits for this variable:

 0 \leq x \leq  2

Variable for inside integration and limits for this variable:

 x \leq y \leq  2
Lo sentimos, la evaluación de la integral falló.
You may try to interchange the order of integration and submit again. (Remember also to adjust limits for integration properly.)

The problem either does not make any sense or it is too difficult for Maxima. Check also, that the integral on the top matches your problem.

Maxima 5.27.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1)                          display2d : false
(%i2) checkon:1
(%i3) f:x*sqrt(1+y^3)
(%i4) opttrigsimp(f):=f
(%i5) vnejsi:x
(%i6) vnitrni:y
(%i7) coor1(m,n):=n
(%i8) coor2(m,n):=m
(%i9) a:0
(%i10) b:2
(%i11) c:x
(%i12) d:2
(%i13) coord1min:-0.5
(%i14) coord1max:1.5
(%i15) coord2min:-0.5
(%i16) coord2max:1.5
(%i17) load("/var/www/maw/integral/simpinvtrigh.mac")
(%i18) load("/var/www/maw/integral2/integral2.mac")
### funkce x\,\sqrt{y^3+1}
 ### 
### vnejsimezea 0
 ### 
### vnejsimezeb 2
 ### 
### vnitrnimezec x
 ### 
### vnitrnimezed 2
 ### 
m 
2 
  
**************************************** 
O.K.: region for integration seems to be well defined 
  
  
**************************************** 
O.K.: trying inside integral 
  
### integration failed