Symbolic Integration: First Stage

Problems that can be solved by the first stage

integrate(x*exp(x^2), x);
					2
				       x
				     %e
      				     ----
				      2
integrate(4*cos(2*x + 3), x);
 			        2 sin(2 x + 3)
integrate(exp(x)/(1 + exp(x)), x);
				       x
      				 log(%e  + 1)
integrate(sin(x)*cos(x), x);
					2
				     cos (x)
      				   - -------
					2
integrate(x*(x^2 + 1)^(1/2), x);
				    2	  3/2
				  (x  + 1)
      				  -----------
				       3
integrate(cos(exp(x))^2*sin(exp(x))* exp(x), x);
				       3   x
				    cos (%e )
      				  - ---------
					3