一类函数不定积分的简捷求法

A simple solution to indefinite integrator of one kind function

本文给出了一类函数不定积分的简捷求法 ,用此法求形如 :∫p (x)u (x)dx,u (x) ″=βu (x) ,β≠ 0 ,p (x)是多项式 ;∫u (x)v (x)dx,u (x) =au (x) ,v (x) =βv (x) ,α≠ -β;∫[u (x) ]3dx,u (x)″ =βu(x) ,β≠ 0等类型的不定积分较方便 ,并给出了理论依据 ,又通过实例指出了方法的具体运用。

This paper presents a solution to a kind of indefinite integrator, which is easier to work out the following such as: ∫ p (x) sin (ax + b) dx, ∫ p (x) cos (ax + b) dx, ∫ p (x) eaxdx, ∫ u (x) v (x) dx (u'' = au, v'' = βv, α + β ≠ 0, ∫ sin3 (ax + b) dx. This paper points out its theoretical basis and the method to apply it with actual illustrations. The result is practical.