Integral of 1/(1 + sinx) ❖ Calculus 1 ❖ Trig Integrals

This video goes through the integral of 1/(1 + sinx). This type of integral is typically found in a Calculus 1 class.

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[oneinabillion]

Thanks! I was stuck on the integral Sinx/(1+Sinx) at the step 1/1+sinx

[Kyle_da_athlete]

Thanks for the video. I finally understand it

[alvegrande]

Umm simplify 1/1+sinx into 1+cscx and get the integral individually.... is this right also?

[Ni]

∫ 1/(1+sin(x)) dx
is undefined at every
-π/2 + 2πn, n is an integer (whenever sin(x) is -1)
tan(x) - sec(x)
is undefined at different points, every
-π/2 + πn (whenever cos(x) is 0)
So -
tan(x) - sec(x)
(sin(x)-1)/cos(x)
(sin(x)-1)cos(x)/cos²(x)
(sin(x)-1)cos(x)/(1-sin²(x))


-cos(x)/(1+sin(x)) + _c_
Making the answer match the possible ranges for the original function.

Not trying to be a smart alec, I really appreciate your channel and your work here! Feel free to delete this comment if it's out of scope for your intended students, I wasn't sure.

[0 to π/4] ∫ 1/(1+sin(x)) dx = 0.5857864...
^ works with either solution

[0 to π/2] ∫ 1/(1+sin(x)) dx = 1
^ works only with the second solution

[hruday]

You could just write sin/(cos^x) as sin/cosx*1/cosx instead of doing substitution in the 4th step