Jim Coroneos' 100 Integrals ~ 029 ~ ∫1/(5 + 3cosx).dx

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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 twenty-ninth problem is to evaluate ∫1/(5 + 3cosx).dx

When we integrate a function that is in the form of a fraction containing a simple trigonometric ratio (and sometimes more than one), the best substitution to use is usually what we call "t formulae" or "half angle formulae."

In a later video series I will be deriving and explaining how to use these formulae in considerably more detail. In this video I simply use them to evaluate the integral.

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Best wishes for your study and your mathematics!

Thank you.

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Swift but quite enjoable presentation of a solution to an example integral. A technique that involves knowledge and final solutuon of some other integral examples in the series, presented so far. Obvioulsy, expressing cos x in termes of t still requires some further elaboration.Thank you for presenting us more and more discoveries, dear Grame!

MrVoayer

Thank you very much - I'd been struggling with this integral and you made it so clear.

MarkFromMullion

Salute u master (sir)
My question is what isRichard Feynman’s Integral Trick and how he invented this trick

And my 2nd question is
Why u r not making new videos for your lovely students
Im waiting for your new video plzzz for god sake

arshantv

What if it is definite on 0-2pi? In this case, the change of the variable is going to change the interval in 0-0. Is the final result 0?

andamariadanciu

Sir Bansi integrated 1 by 4+secx please down my answer

shootmegaming

1/(4+t^2) = 1/4 * 1/(1+t^2/4)
1/(4+t^2) = 1/4 * 1/(1+(t/2)^2)
1/(4+t^2) = 1/2 * (1/2)/(1+(t/2)^2)

holyshit

Muze all internal lesson ke all video chahiye

aniketmehar

Jim Coroneos' 100 Integrals ~ 029 ~ ∫1/(5 + 3cosx).dx

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

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

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

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

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

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

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

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

Jim Coroneos' 100 Integrals ~ 018 ~ ∫1/[x√(a²-x²)].dx

Jim Coroneos' 100 Integrals ~ 011 ~ ∫x/[(x+4)(x+2)].dx

Jim Coroneos' 100 Integrals ~ 031 ~ ∫sinx/(5 + 3cosx).dx

1-10 OF JIM CORONEOS' 100 INTEGRALS SOLVED!

Jim Coroneos' 100 Integrals ~ 029 ~ ∫1/(5 + 3cosx).dx

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

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

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

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

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

Jim Coroneos' 100 Integrals ~ 010 ~ ∫x³/(x² + 1).dx

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

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

Jim Coroneos' 100 Integrals ~ 014 ~ ∫x³/(2x-1).dx

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

Jim Coroneos' 100 Integrals ~ 006 ~ ∫cos²(x/2).dx