Can We Integrate All Continuous Functions?

In my earlier videos I went over a useful strategy for integration but with that a very important question arises: can we use our integration strategy to integrate all continuous functions? The answer to that question is unfortunately NO, well at least not in terms of the regular elementary functions. In this video I go over what elementary functions are and explain how most elementary functions, such as e^(x^2) can not be integrated in terms of basic elementary functions. One method to prove whether or not a function can be integrated in terms of elementary functions is called the Risch Algorithm and was developed in 1968 by the American Mathematician Robert Henry Risch.

In my later videos I will go over how functions such as e^(x^2) can be integrated in terms of infinite series so stay tuned for that!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhd4iIg7HrqROZAvF2w

Related Videos:

Strategy for Integration: Examples 2 to 5: http://youtu.be/3JGU3vJsPIk Strategy for Integration: Example 1: http://youtu.be/xqwRpvdrD6Y Strategy for Integration: http://youtu.be/7JxW2N7izF0 Integration by Partial Fractions: http://youtu.be/r07NnKf76og Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo Integration by Parts: Proof: http://youtu.be/TZhEOct5u_M The Substitution Rule for Integrals: http://youtu.be/VsLC-0g6hVg Trigonometric Integrals: Guidelines for sin(x)cos(x): http://youtu.be/aE8Sz5BdMT8 Trigonometric Integrals: Guidelines for tan(x)cos(x): http://youtu.be/oz5nXlYQPB0 .

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