Hi im having trouble on where to start, im trying to itegrate sin(x)/cos^2(x). Should i make a u subsitution, if so for what?

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- May 18th 2008, 12:51 PMcowboys111help integrating
Hi im having trouble on where to start, im trying to itegrate sin(x)/cos^2(x). Should i make a u subsitution, if so for what?

- May 18th 2008, 12:52 PMMoo
- May 18th 2008, 01:06 PMChris L T521
- May 18th 2008, 01:09 PMcowboys111
cool thank you!!

- May 18th 2008, 01:13 PMMoo
- May 18th 2008, 01:26 PMgalactus
I have had several tell me that in Europe they do not deal with sec,csc,cot at all.

Wonder why?.

For your benefit. Their derivatives:

$\displaystyle \frac{d}{dx}[csc(x)]=-cot(x)csc(x)$

$\displaystyle \frac{d}{dx}[cot(x)]=-csc^{2}(x)$

$\displaystyle \frac{d}{dx}[sec(x)]=tan(x)sec(x)$ - May 18th 2008, 01:28 PMMoo
In France, we've never seen such formulae... Only dealing with cos, tan, sin, and that was enough ^^ (in my high school...can't tell about all the others). Why ? I don't know, maybe because cot, csc, sec are known with sin, cos, tan... ~

It's the same for the substitution. It seems that for you it's common to substitute, but here, we just recognize the derivative and apply formulae of antiderivatives we know :p

Actually, by "here" in my previous post, I meant the equality of Chris where an antiderivative of sec*tan is sec..

Edit : thanks a bunch ! - May 18th 2008, 01:32 PMgalactus
In my previous post, I went ahead and posted the derivatives of those functions.

- May 18th 2008, 01:38 PMgalactus
Here are their antiderivatives, Moo:

$\displaystyle \int{cot(x)}dx=ln(|sin(x)|)+C$

$\displaystyle \int{sec(x)}dx=ln(|sec(x)+tan(x)|)+C$

$\displaystyle \int{csc(x)}dx=ln(|csc(x)-cot(x)|)+C=ln(|tan(\frac{x}{2})|)+C$ - May 18th 2008, 01:41 PMMoo
Really weird stuff :D

Thanks (Wink) - May 18th 2008, 01:43 PMgalactusQuote:

Why ? I don't know, maybe because cot, csc, sec are known with sin, cos, tan... ~

One thing I noticed about calculators that do have them (such as the Voyage 200, TI-92, TI-89), they have the functions but only display in terms of sine and cosine. For instance, if you wanted the antiderivative of sec(x), the calculator displays it as $\displaystyle ln(\frac{-cos(x)}{sin(x)-1})$ instead of

$\displaystyle ln(sec(x)+tan(x))$ - May 18th 2008, 04:55 PMChris L T521