Jim Coroneos' 100 Integrals ~ 005 ~ ∫sinx.sec³x.dx (Three Methods)

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Partly to honour Jim, and partly to fulfil an international need, I have decided to produce 100 videos, showing how to solve his 100 integration 'problems.' I hope you find the videos useful!

This is the second video that I have created in order to evaluate this integral. The first one suffered because I chose to use the opportunity to discuss a particular method for solving integrals (by structuring them as derivative patterns). Admittedly, this is not the only method and, arguably, not the fastest or 'easiest.'

I therefore decided to create this video showing three common/popular methods for evaluating integrals of this kind. In my experience as a teacher, a typical large class would find groups of students who would prefer each of these methods. They are all mathematically correct but different methods will appeal to different students according to their strengths and how they think.

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Best wishes for your study and your mathematics!

Thank you.

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Valuable explanation and enlightening teaching of how to think and how to connect integral and derivative. It requires some practice to become versed in various methods but it is important to stay open minded and be prepared to accept other possibilities. "u substitution" is probably the most widely used "by the book" method of solving this particular integral. But two other methods are more than valid.Thank you, Greame, for broadening our knowledge.

MrVoayer

Hi I was just wondering if you can put the same integral in the form: [tan(x)xsec^2(x)]dx and integrate from there. I tried doing this and got a different answer. I don't know if I did it wrong or if there is a reason you cannot do it this way. Thanks!

jazcreations

Jim Coroneos' 100 Integrals ~ 005 ~ ∫sinx.sec³x.dx (Three Methods)

Jim Coroneos' 100 Integrals ~ 030 ~ ∫1/(3 + 5cosx).dx

Jim Coroneos' 100 Integrals ~ 015 ~ ∫(1+x)/√(1-x-x²).dx

Jim Coroneos' 100 Integrals ~ 021 ~ ∫(cos‾¹x)/√(1-x²).dx

1-10 OF JIM CORONEOS' 100 INTEGRALS SOLVED!

Jim Coroneos' 100 Integrals ~ 016 ~ ∫1/[x²√(1-x²)].dx

Coroneos' 100 Integrals: 050 ∫(x^3)(4+x^2)^(-1/2).dx

Jim Coroneos' 100 Integrals ~ 025 ~ ∫1/[x²(1-x)].dx

Jim Coroneos' 100 Integrals ~ 027 ~ ∫1/(1+x²)².dx

Coroneos' 100 Integrals: 052 ∫(x^2)/(1-x^4).dx

Jim Coroneos' 100 Integrals ~ 005 ~ ∫sinx.sec³x.dx (Three Methods)

Jim Coroneos' 100 Integrals ~ 020 ~ ∫x/(√x+1).dx

Jim Coroneos' 100 Integrals ~ 032 ~ ∫1/(1 + cos²x).dx

Jim Coroneos' 100 Integrals ~ 028 ~ ∫tan³x.dx

Jim Coroneos' 100 Integrals ~ 009 ~ ∫tan‾¹2x.dx

Jim Coroneos' 100 Integrals ~ 023 ~ ∫1/[x(lnx)³].dx

Jim Coroneos' 100 Integrals ~ 026 ~ ∫1/[x²(1+x²)].dx

Jim Coroneos' 100 Integrals ~ 001 ~ ∫x/(x²+4).dx

Jim Coroneos' 100 Integrals ~ 022 ~ ∫√[(x+1)/(x-1)].dx

Jim Coroneos' 100 Integrals ~ 004 ~ ∫sinx.cos³x.dx

Jim Coroneos' 100 Integrals ~ 005 ~ ∫sinx.sec³x.dx

Coroneos' 100 Integrals: 002 ∫x/√(x²+4).dx

Jim Coroneos' 100 Integrals ~ 019 ~ ∫1/[x√(x²-a²)].dx

Jim Coroneos' 100 Integrals ~ 017 ~ ∫1/[x√(a²+x²)].dx

Jim Coroneos' 100 Integrals ~ 008 ~ ∫x.sec²2x.dx