These 1 D integration utilities are NOT dissociative
Mathcad/Mathsoft offers [Adaptive, Romberg, Infinite, Singular]
Native Smath only Simpson.
At this point, we can improve Smath 1 D integration
1. Ordinary Simpson ... ODE integrators.
Both range from ~ exact, very good [acceptable] ... glorious freak.
2. FD [Finite Differences] not recommended Infinite/Singular.
3. ʃkernel(f,a,b,n) ... ∫Adaptive(f,a,b,ε) ... ∫simplex(f,a,b,s).
4. Don't forget maple companion !
Take ... Jean.

Integration Utilities_0 NONlinear.sm (14 KiB) downloaded 85 time(s).
Integration Utilities_0 Infinite_Singular.sm (148 KiB) downloaded 81 time(s).
Integration Utilities_0 NONlinear Splines Copy.sm (121 KiB) downloaded 73 time(s).
Integration Utilities_0.sm (241 KiB) downloaded 82 time(s).