In[]:=
Integrate[Sqrt[x^4+x]/(2x^3+1),x]//Simplify[#,x>0]&
Out[]=
1
3
ArcTan1+2
3
x
+2
3
x
+
6
x
+Log
3/2
x
+
1+
3
x

In[]:=
FunctionExpand[(2xSqrt[x+x^4]AppellF1[1/2,-1/2,1,3/2,-x^3,-2x^3])/(3Sqrt[1+x^3])]​​D[%,x]//FullSimplify[#,x>0]&
Out[]=
2x
x+
4
x
AppellF1
1
2
,-
1
2
,1,
3
2
,-
3
x
,-2
3
x

3
1+
3
x
Out[]=
x+
4
x
1+2
3
x
In[]:=
$CloudVersion
Out[]=
1.70.1 (December 30, 2024)