1. does macsyma have a recognizer for bessel integrals such as integral(cos(x*sin(u)),u,-%pi,-%pi) 2. how can i compute the inverse laplace transform of 1/sqrt(1+s^2). when i try to execute integral(exp(z*s)/sqrt(1+s^2),s,a-%i*inf, a+%i*inf) i get the error that limits of integration must be real. 3. is there a way to compute termwise, the integral of a powerseries? 4. in using closedform to sum sum(q^n*x^2n*(-1)^n/n!,n,0,inf) i got the error taylor found a essential singularity. this is just the series for exp(q*x^2). 5. i have a series sum(x^(2*n)/(sqrt(1+x^2)*n!), n, 0, inf) and i want to integrate term by term between 0 and 1. i have a reduction formula for integral(x^n/sqrt(1+x^2) which is x^m*sqrt(1+x^2)/m + integral(x^(n-2)/sqrt(1+x^2)). how can i get macsyma to apply the reduction formula to the series to convert it to a double series. 6. how can i find out which integrals macsyma can recognize.