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That is, I think the author of the question is spot on to the current state in mathematics education. I have a firmly held thought that within twenty years no mainstream calculus text will contain a chapter on techniques of integration. The wide availability of computer algebra systems have made those topics obsolete for the most part. (Of course they will be great topics for Mathematics Education courses and courses in the History of Mathematics.) That is, I think the author of the question is spot on to the current state in mathematics education. I have a firmly held thought that within twenty years no mainstream calculus text will contain a chapter on techniques of integration. The wide availability of computer algebra systems have made those topics obsolete for the most part. (Of course they will be great topics for Mathematics Education courses and courses in the History of Mathematics.) Obsolete, hardly. There are many integrals that would require trigonometric/hyperbolic substitution that can't be solved using a geometric interpretation. And the use of a CAS in those situations is just plain lazy and irresponsible. How would they be programmed in future if everyone thought the method of solution was "obsolete"? That is, I think the author of the question is spot on to the current state in mathematics education. I have a firmly held thought that within twenty years no mainstream calculus text will contain a chapter on techniques of integration. The wide availability of computer algebra systems have made those topics obsolete for the most part. (Of course they will be great topics for Mathematics Education courses and courses in the History of Mathematics.) I think in what passes for the real world they have been out of date for far longer. In fields that actually use such integrals it has been virtually universal practice to look them up in tables since before I started work outside of a university in the late 70's.
