Abstract
We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for elementary functions. Certain integrals, including improper integrals, can be calculated using numerical algorithms. In this case, every user has the ability to indicate the required accuracy with which he needs to know the numerical value of the integral. We highlight special functions allowing us to calculate complete elliptic integrals. These include functions for calculating the arithmetic-geometric mean and the geometric-harmonic mean, which allow us to calculate the complete elliptic integrals of the first kind. The set also includes the modified arithmetic-geometric mean, proposed by Semjon Adlaj, which allows us to calculate the complete elliptic integrals of the second kind as well as the circumference of an ellipse. The Lagutinski algorithm is of particular interest. For given differentiation in the field of bivariate rational functions, one can decide whether there exists a rational integral. The algorithm is based on calculating the Lagutinski determinant. This year we are celebrating 150th anniversary of Mikhail Lagutinski.
Highlights
The development of computer algebra systems and cloud computing makes it possible to solve many computational problems
Free access to the MathPartner service is possible at http://mathpar.ukma.edu.ua/ as well as http://mathpar.com/
To calculate the indefinite integral of an elementary function f(x) one can run the command int(f)dx, where x is declared in the environment SPACE
Summary
The development of computer algebra systems and cloud computing makes it possible to solve many computational problems. He developed new algorithms for solving problems in mathematical physics and implemented them in many well-known systems of computer algebra. He has worked on systems such as REDUCE, Mathematica, Maple, and Singular. Many general computer algebra systems today support symbolic integration of elementary functions. They all have a common drawback that is the incompleteness of solving the problem of symbolic integration. Commercial systems do not give users access to their packages of procedures, and they do not have specialists who can complete the theory of calculating the antiderivative for the composition of simple elementary functions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
