几类可用倒代换求其不定积分的函数

Several Kinds of Available Back Substitution for Function of the Indefinite Integral

现行教材和文献仅应用倒代换求出了∫槡a-x2d等x4dx、∫x和x槡4-x2∫dx x4(1+x2不定积分,对应用倒代换求)不定积分并没有进行深入研究和探讨,更没有得到普遍性的结论.为此,根据被积函数的特点,研究了应用倒代换求其不定积分的适用性,给出了可用倒代换求其不定积分的几种函数类型,包括被积函数为111、x(a+bxα、)xn(1+x2、)xα+1(a+bxα)1和1n+1xα+11+x2α(1+xn)n等情形,并得到了一些相应的结论.

Abstract： The current textbooks and documents only got the indefinite integrals such asa2-x2/4xds、dxx4-x2and dx/x4（1＋x2based on the back substitution. However, there is no further study and even no general consequence. The features ofthe integrand offers the applicability of the application of back substitution for its integral. Then several types available for the recip-rocal substitution function integral are given, including the integrand such as1/x（a＋bx^α）、xn（1/1＋x2）、1/xa＋1（a＋bx^α）、1/xα＋1＋x2α和1/（1＋xn）n＋1/nSome conclusions were obtained.