Integral of cosec (1 Viewer)

[matt_17]

What is the integral of cosec x dx?
I have 2 textbooks that have different answers:
1. ln (cosecx - cotx)
2. -ln (cosecx + cotx)

 

[Slidey]

ln(tan(x/2))

 

[Slidey]

PLUS A CONSTANT!!!1

Of course, that's not to say that the two answers you gave aren't correct. They are. In fact, all three answers are correct. If you want proof, differentiate.

 

[Jase]

They're the same..
but my gad i cant differentiate Cosec x .. its all so confusing!! its -cosecx.cotx right?

Well i'd stick to ln(cosecx - cotx)...

 

[withoutaface]

In future to check the answer you can try substituting a few values, if they give the same solutions for the same values of x, chances are the answers are the same.

 

[Estel]

Just differentiate your damn answer!

 

[Heinz]

1/(cosecx + cotx)
= (cosecx - cotx)/(cosec²x - cot²x)
= (cosecx - cotx)/([1 - cos²x]/sin²x)
= cosecx - cotx

In short, log rules are your friend

 

[matt_17]

thanks for your help. I differentiated it and got ln (cosecx - cotx). I've subbed in values and found that they were the same.