The Expression Calculator is no rival to this software. The value of integrals is an approximation, even if in most cases all decimals shown are found to be exact. The Expression Calculator uses the Tegral embedded quadrature formulas method. The main idea is to approximate the functions' integrals with an order 30 quadrature formula, which is calculated using Legendre's orthogonal polynomials. Two embedded quadrature formulas are extracted from the order 30, one of order 14 and another of order 6.
All formulas are symmetric.
The integral for the elementary interval is calculated from the order 30 quadrature formula, the maximum errors committed during the calculation using the other two. If the error committed satisfies the given tolerance, the integral's value is kept as final. If not, the interval is divided into two equal parts and the Gauss integral is calculated again. In case the sum of the absolute values of all errors does not match the tolerance, Tegral will look for the interval that has the worst error and divide it into two parts. The algorithm recurses until a tolerated error value is reached.