Question 1183905
{{{int(xlnxsinx,dx)}}}.

Use IBP.  Let u = lnx,  dv = xsinxdx


===> du = dx/x and v = -xcosx + sinx (which you can also get through IBP).

===> {{{int(xlnxsinx,dx) = ln(sinx - xcosx) + int((xcosx+sinx), dx/x) = 
ln(sinx - xcosx) +  int((xcosx+sinx), dx/x)  = ln(sinx - xcosx) +  int(cosx, dx) + int(sinx/x,dx) }}}


= {{{ln(sinx - xcosx) +  sinx + int(sinx/x,dx)  =  ln(sinx - xcosx) +  sinx + Si(x)}}}.


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Next time, if you want to do integration of functions, try Wolfram Alpha or Symbolab first.  


You'll get a faster answer and solution there than you can type your question here.