# Whats the primitive function of $f(x) = x\frac{\cos(x)}{\sin(x)}$? [closed]

Whats the primitive function of

$$f(x) = x\frac{\cos(x)}{\sin(x)}$$

$$F(x) =$$

Im trying to figure out how perspective distorts on a continuous scale because i need it for drawing space art. Since there's little close up shots of space I need to get some reference through math to compare and to draw oultlines.

This is a fraction of what ive tried on and off past year, most recently the first link. I think I might be getting closer but dont know for sure. Stuck at understanding primitive function.

http://imgur.com/a/RIJDOdH

http://imgur.com/a/lQzW0ry

I almost have a degree in engineering but my math skill is more of high school

When i get acces to a computer i will incorperate the text from pictures to this body of text and only link the pictures. If i get enough reputation ill upload pictures here too so that Its collected. And post this for now since i dont have computer.

There is some indirect general interest in what this question is about from other drawers and painters

Plz if you have the time and want to, write the primitive function and how you got it, to novice

? /Johan

## closed as off-topic by Jyrki Lahtonen, RRL, Hans Lundmark, Nosrati, CesareoJan 20 at 13:25

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• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Jyrki Lahtonen, RRL, Hans Lundmark, Nosrati, Cesareo
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• $$\int \frac{x\cos(x)}{\sin(x)}dx=x\ln(1-e^{2ix})-\frac12 i\left(x^2+\text{Li}_2(e^{2ix})\right)+C$$ – JJacquelin Jan 20 at 7:28
• Please check out our guide for new askers. – Jyrki Lahtonen Jan 20 at 7:29
• Sure looks like there's no elementary primitive. What is the problem you want to solve? – Jyrki Lahtonen Jan 20 at 7:32
• Thx Jyrki Lahtonen – Johan Östberg Jan 20 at 12:57
• This became an involontary bump of old question when adding context to what i thought was irrelevant information to a one solution problem. Sorry – Johan Östberg Jan 20 at 12:59

## 1 Answer

Using series $$\cot(x)=\sum_{n=0}^\infty\frac{(-1)^n\, 2^{2 n}\, B_{2 n} }{(2 n)!}\,x^{2 n-1}$$ $$x\cot(x)=\sum_{n=0}^\infty\frac{(-1)^n\, 2^{2 n}\, B_{2 n} }{(2 n)!}\,x^{2 n}$$ $$\int x\cot(x)\,dx=\sum_{n=0}^\infty\frac{(-1)^n\, 2^{2 n}\, B_{2 n} }{(2n+1) \,(2 n)!}\,x^{2 n+1}$$

• Thx for answer. I dont understand, its to advanced math for me or what to say – Johan Östberg Jan 20 at 13:02