Solve Improper Integral of 1/(1+(tanx)^sqrt(pi)) from 0 to pi/2

[SeReNiTy]

Hi i am completely stuck on a intergration problem, i have tried substition, and every technique i can think off but i cannot solve it. It is a improper intergral and the answer is pie/4

The question is:

find the intergral with limits upper pie/2 and lower 0

1/(1+(tanx)^sqaureroot pie).dx

P.S: how do i type equations liek the way some ppl do in their threads

 

[whozum]

$$\int\frac{1}{1+tan^{\sqrt{e\pi}}(x)}{dx}$$

Is that the right integral? Clicking the graphic will show you the code to type it.

 

[Gamma]

Following thread was about how to write mathematical stuff using Latex. Very nice. Have it in your favorites if you are going to post a lot. Click anyone of those equations/expressions to find the Latex tag.

https://www.physicsforums.com/showthread.php?t=8997&highlight=latex

 

[dextercioby]

Okay.Here's the antiderivative

$$\int \frac{dx}{1+\tan^{\sqrt{\pi}} x}$$


(v.attachement).

Now,u can see that,both in the lower limit & in the upper one,u need to compute the limits in ivolving the $$_{2}F_{1}$$ of an adorable argument & tangent of "x" to a weird power.

Good luck with those limits...

Daniel.

 

[Data]

and by the way, $\pi$ is spelled "pi." :)

 

[dextercioby]

I like "pie"...Yumm-Yumm :!) (Please work on that Latex code,will u?People are confused because of your weird notations).

Daniel.

 

[Nylex]

There's also only 1 r in both "integration" and "integral".

 

[dextercioby]

And it's "...think of"... And "like" (sic!)...


Daniel.


P.S.Another piece of advice:use the spell checker.

 

[whozum]

Its "Another PIECE OF advice" :-D

 

[SeReNiTy]

Thanks so much guys, wow you guys run a real good service. Oh, and thanks for the correction, of course how stupid was i to write "pie", indeed it is "pi".

 

[SeReNiTy]

$$\int\frac{1}{1+tan^{\sqrt{e\pi}}(x)}{dx}$$

Is that the right integral? Clicking the graphic will show you the code to type it.

No, this is the integral $$\int \frac{dx}{1+\tan^{\sqrt{\pi}} x}$$
Oh, and to the dexter, could you clarify what steps you took reach the antiderrivative? Like substitution or interation by parts?

 

[Data]

He got mathematica to do it. I find it extremely unlikely that it is possible to express the antiderivative in terms of elementary functions. In what context did this integral appear?

 

[SeReNiTy]

He got mathematica to do it. I find it extremely unlikely that it is possible to express the antiderivative in terms of elementary functions. In what context did this integral appear?

Oh, so he used a computer program or something? So this integral cannot be expressed with elementary functions?

 

[dextercioby]

Well,it cannot.If u decide to include hypergeometric functions among elementary functions,then u might say it is,else,not.

Now,if u plot the functions

$$\frac{1}{1+\tan^{\sqrt{\pi}}x}$$ & $$\frac{1}{1+\tan^{2}x}$$ on the interval $$[0,\frac{\pi}{2})$$

,then,by evaluating the integral of the second function on the same interval (which is very,very easy),u might get an approximation to the first integral.If u have a software that could plot them together in the same picture/graph,it would be perfect.

Daniel.