Values of some integrals



My knowledge of Mathematica syntax isn't great, but I think this is
correct.


Pete Gustafson




---
In[37]:= Integrate[x^(2*I+3)/Exp[I*x^3/2],{x,0,Infinity}]

                              3 + 2 I
                             x
Integrate::idiv: Integral of -------- does not converge on {0,
Infinity}.
                                   3
                              I/2 x
                             E

                    3 + 2 I
                   x
Out[37]= Integrate[--------, {x, 0, Infinity}]
                         3
                    I/2 x
                   E

---
In[38]:= Integrate[x/(sinh[x]-I),{x,-Infinity,Infinity}]

                        x
Out[38]= Integrate[------------, {x, -Infinity, Infinity}]
                   -I + sinh[x]

---
In[39]:= Integrate[x^3*Exp[I*x^3/2],{x,0,Infinity}]

                                   3
                              I/2 x   3
Integrate::idiv: Integral of E       x  does not converge on {0,
Infinity}.

                         3
                    I/2 x   3
Out[39]= Integrate[E       x , {x, 0, Infinity}]

---
In[40]:= Integrate[x^2*Exp[I*x^3/2],{x,0,Infinity}]

                                   3
                              I/2 x   2
Integrate::idiv: Integral of E       x  does not converge on {0,
Infinity}.

                         3
                    I/2 x   2
Out[40]= Integrate[E       x , {x, 0, Infinity}]

---
In[41]:= Integrate[x^k*log[x]/(x+3),{x,0,Infinity}]

                    k
                   x  log[x]
Out[41]= Integrate[---------, {x, 0, Infinity}]
                     3 + x









On Tue, 2006-03-14 at 17:55 -0500, Raymond Toy wrote:
> Could someone with macsyma/mma/maple evaluate the following integrals
> for me?  I'm verifying some of the defint routines and I'd like some
> independent verification of these integrals.
> 
> integrate(x^(2*%i+3)/exp(%i*x^3/2),x,0,inf);
> 
> integrate(x/(sinh(x)-%i),x,minf,inf);
> 
> integrate(x^3*exp(%i*x^3/2),x,0,inf);
> 
> integrate(x^2*exp(%i*x^3/2),x,0,inf);
> 
> integrate(x^k*log(x)/(x+3),x,0,inf);
> 
> Thanks,
> 
> Ray
> 
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