Calculus Where Can I Find More Challenging Integrals for My Competition?

[Mondayman]

Hi folks,

I love doing integrals, and I think I'm going to start a competition at my school. The integrals in the standard calculus textbooks I have access to, Briggs, Stewart, etc., are pretty elementary. I am looking for some harder integrals. I have the books Irresistible Integrals and Inside Interesting Integrals already, and I've found some good ones browsing through this forum and online. I was thinking maybe older textbooks would a good place to look. I was wondering if anyone has worked through any that they found hard, or if anyone knows where I can find some harder integrals?

 

[fresh_42]

You could look into our Challenge thread (filter "Challenge" in the General Math forum). There are quite a few integral questions.

 

[jedishrfu]

There’s a Schaums Outlines with many worked and not worked examples for Calculus that you could use. They also have a Handbook Of Math Formulas with many challenging but no method on how to solve them. People look up the integral they have and do the substitutions to get the answer.

There’s a YouTube channel called BlackPenRedPen that shows an integral and then solves it. They are usually somewhat unusual integrals too.

 

[ibkev]

You might also enjoy this:

https://www.amazon.com/dp/B014P9HVHQ/?tag=pfamazon01-20

 

[Mondayman]

You could look into our Challenge thread (filter "Challenge" in the General Math forum). There are quite a few integral questions.

Thank you, there are some pretty hard ones on here.

There’s a Schaums Outlines with many worked and not worked examples for Calculus that you could use. They also have a Handbook Of Math Formulas with many challenging but no method on how to solve them. People look up the integral they have and do the substitutions to get the answer.

There’s a YouTube channel called BlackPenRedPen that shows an integral and then solves it. They are usually somewhat unusual integrals too.

I never thought to pull them out of a handbook and work it out, that's a fantastic idea.

You might also enjoy this:

https://www.amazon.com/dp/B014P9HVHQ/?tag=pfamazon01-20

I have this book already, its what got me interested in solving tricky integrals.

I appreciate the replies, its been helpful.

 

[jedishrfu]

Also you should collect together the various recipes people have used to solve more intractable ones.

Theres a youtuber blackpenredpen who solves many kinds of integrals using a variety of tricks.

Parametric differentiation was one such trick that I never learned and was amazed that you could even do it.

https://en.m.wikipedia.org/wiki/Parametric_derivative

 

[MidgetDwarf]

The Feynman method?

 

[jedishrfu]

Yes, only Feynman learned it from his Physics teacher's book reference:



I learned of it only recently from Prof Nearing Math Methods book:

http://www.physics.miami.edu/~nearing/mathmethods/mathematical_methods-three.pdf
As an aside, since we're talking about the Teacher We Never Had:

https://www.microsoft.com/en-us/res...nman/?from=http://research.microsoft.com/tuva