Numerical integration methods

[Albert Chan]

When I tried this, integral gives an warning "Adaptive method failure, will try with Romberg ..."
So, the trick is to "adapt" manually, by splitting the integral.

CAS> f(x) := x^2 * expm1(1/x^3)
CAS> int(f(x), x, 1., 20.), int(f(x), x, 20., 100.)

[3.19558488078, 1.60945857854]

∫ + ∫ = 4.80504345932

Udpate:

I increased HOME eps setting to 1e-9 (default was 1e-12)

CAS> int(f(x), x, 1., 100.)

4.80504345904

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I had translated robve's double exponential quadrature code for HP Prime, here

CAS> quad(f, 1, 100)

[4.80504346031, 4.01306988706e−11]

quad(f,a,b) was defaulted with eps = 1e-9, thus slight error on last digit.

CAS> quad6(f, 1, 100, 1, 6, 1e-12)

[4.80504346032, 1.28096166025e−13]