Osittaisintegrointi
Osittaisintegrointi, known in English as integration by parts, is a method used in calculus to find integrals of products of functions. It is derived from the product rule for differentiation. The product rule states that the derivative of a product of two functions, u and v, is given by (uv)' = u'v + uv'. Integrating both sides of this equation with respect to x yields uv = ∫u'v dx + ∫uv' dx. Rearranging this equation, we get ∫uv' dx = uv - ∫u'v dx. This is the fundamental formula for integration by parts.
The practical application involves choosing one part of the integrand to be u and the other to
Integration by parts is particularly useful for integrating products of different types of functions, such as