How can integral of (cos(4x))/(sin(2x)*cos(2x)) has different result with integral of 2*cot(4x)?
Whereas both of them are the same, just different form.

Chen Jang T. | MaCT (Math and Chemistry Tutor)MaCT (Math and Chemistry Tutor)

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They are essentially the same function. I think both answers should be zero. Only the first integral question utilize more complex approximation, but the answer is not that much different. −1.110223024625157×10^{−16} = -0.0000000000000001≈0

Pierce O. | Graduate Mathematics Student, Will Tutor Any Math SubjectGraduate Mathematics Student, Will Tutor...

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Hi R,

They are not the same function. If you are unsure, graph them.

Neither integral is difficult to calculate. The first integral, for cos(4x)/(sin(2x)cos(2x)), try looking at ln(sin(2x)cos(2x)), and be sure you remember the trig identity cos(2u)=cos^{2}(u)-sin^{2}(u).

The second integral is just a substitution problem. Best luck

But, I think you made a mistake. You said that they are not the same function and you asked me to graph them.
In fact, I graphed them and found that both of them are really the same function.

We can use any graph program to prove that and we will always get the same result.
I use this site: graphsketch.com.

## Comments

Thank you very much, Chen Jang.