Can computers solve all integrals?

Integral calculator with calculation path

The calculator understands the following constants. These variables are recognized when they are entered:

  • e = Euler number (2.718281 ...)
  • pi, π = circle number (3.14159 ...)
  • phi, Φ = the golden ratio (1.6180 ...)
  • d, t, u andv are used internally for substitutions and partial integration (please exchange this variable for another)

The integral calculator uses the same syntax as modern graphical pocket calculators. Implied multiplication (5x = 5 * x) is recognized. However, if syntax errors occur, it is better to avoid implicit multiplication and to rewrite the input. To enter powers, you can alternatively use two multiplication signs (**) instead of the exponent sign (^): x5 = x ^ 5 = x ** 5. The input can be made either via the computer keyboard or via the normal keyboard of the computer or mobile phone.

The integral calculator calculates bothdefinite as well as indefinite integrals. Numbers, fractions and variables can be used as integral limits. It is not always possible to carry out a step-by-step calculation for all integrals. If so, the calculator will still try to find the integral. A corresponding message is also displayed. For certain integrals whose antiderivative could not be found, the integral calculator will attempt a numerical approximation. The integral computer then also displays a corresponding message.

The computer decides for itself which integration method would be best and solves the integral just as a human would. The following integration procedures for determining the antiderivative are supported by the computer:

It may be that more options there to solve an integral. In this case, the various solutions are calculated and also displayed.

Should the computer not be able to calculate the calculation path, the software will still try to determine the integral.