How do I solve this indefinite integral


Integration tasks emerge quite often in engineering problems, here first integrals of the form

(indefinite integral) resp. (definite integral)

to be viewed as. The task of solving an indefinite integral is to find what is known as one Indefinite integralF (x), the derivative of which is the integrand y (x). This problem (occurs in technical mechanics, for example, when calculating bending lines) is comparatively rare in engineering mathematics, the far more common case is the solution of a certain integral, which in mathematics training, however, usually involves the solution of the associated certain integral begins.

For the Solution of indefinite integrals It used to be the case for engineers: You can find the solution in extensive integral tables, or you can't find it at all. This is different today: The programmers of symbolic mathematics software (Maple, Derive, Mathematica, ...) have seen their ambition in this area in particular to allow all indeterminate integrals for which a closed solution exists (not for every integrand even find an antiderivative) to actually solve. In the textbook "Dankert / Dankert: Technical Mechanics", the problem of solving integrals is discussed for the first time in the chapter "Focus points" as the integrals

Pop up. These can of course also be solved "by hand" using the means known from mathematics training (basic integrals, partial integration). The adjacent screen snapshot shows that the solution of the indefinite integrals can also be transferred to a symbolic mathematics program (the Maple script is available for download as UnbInt.mws).

For the Solution of certain integrals applies to the engineer: The problem can be considered solved if the definite integral is correctly written down. The ambition to go the "classic solution" (solving the indefinite integral and then inserting the integration limits) should be kept within limits or reserved for symbolic mathematical programs that usually try this path first.

When calculating certain integrals, nothing speaks against numerical integration. The Internet site "Mathematics for Technical Mechanics" includes an extensive area "Numerical Integration" that deals with all important aspects of this topic. In general, however, the engineer can rely on the powerful tools available. The example given above for indefinite integration was also taken from a problem with definite integrals. This is solved with the support of various software products on the page "Example of centroid calculation".