Integral of 1/sin x ❖ Calculus ❖ Trig Integrals

This video goes through the integral of 1/sin x. This type of integral would typically be found in a Calculus 1 class.

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[Anonymous_Ali]

Why we don't write 1/sinx = cosecx
Directly inside integral and then take integration of cosecx

[seegeeaye]

1/sinx = 1/(2sin(x/2) cos(x/2) = 1/2((sec(x/2))^2/(tan(x/2)). So we have the integral of d((tanx/2)/(tanx/2) = ln (tanx/2) + C. We forget the "U business" and it makes simpler

[experiencethebeats]

Thanks! Definitely lots of substitutions.

[sirisaacnewton]

Always enjoy watching your integral videos! Thanks for posting them.

[Sgth]

This is a beautiful way of proving the natural log of the half identity of tanx with the integral of cscx. All with an interesting u substitution

[DeepakGupta-cmbx]

Thank U som much for the detailed explanatioin. Let this be a training lesson for other teachers

[yilinlai]

Thanks so much, this helps me a lot ! Thank you !

[johnholemans]

Thank you for this . Although, My textbook sais integral of Tan(x) = ln[sec (x) ] +c

[TheBaluchiterium]

The integrals over tan u and cot u do not have to be memorized. They are easily calculated, e.g. by integrating tan u = sin u / cos u and making the substitution z = cos u. Similar method for the cot u.

[garyward]

Do you ever go down a wrong path or does the method to use for a solution just seem obvious to you every time?

[alondrarivera]

Can you explain why x equals 2u? I would never reach that step on my own and I don't understand why

[JY-rv]

Since sin square x plus cos square x equal to 1. Why not integrate sin square x plus cos square x over sin x for the first step?

[duke_of_oz]

Nice pick-up line ... I'm gonna' let my x equal 2 u

[bradvincent]

Squeaking sound in the background was annoying