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- Improper integral
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How to use it?
- Integral of d{x}:
- Integral of x/sinx
- Integral of sqrt(1+cosx)
- Integral of x/(x-1)^2
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Integral of 1/(2+cos(x))
- Derivative of:
- 1/(2+cos(x))
- Limit of the function:
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1/(2+cos(x))
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Identical expressions
- one /(two +cos(x))
- 1 divide by (2 plus co sinus of e of (x))
- one divide by (two plus co sinus of e of (x))
- 1/2+cosx
- 1 divide by (2+cos(x))
- 1/(2+cos(x))dx
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Similar expressions
- 1/((x)^1/2+cosx^2)
- 1/(2-cos(x))
- 1/2+cos(x)
- 1/((2+cosx)×(sinx))
- (a+1)/(2*x^(1/2))+cos(x+b)
- 1/(2+cosx)^2
- 1/(2+cosx)
Integral of 1/(2+cos(x)) dx
The solution
You have entered
[src]
1 / | | 1 | ---------- dx | 2 + cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\cos{\left(x \right)} + 2}\, dx$$
Integral(1/(2 + cos(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| |\/ 3 *tan|-|||
/ ___ | |2 2 | | \2/||
| 2*\/ 3 *|pi*floor|------| + atan|------------||
| 1 \ \ pi / \ 3 //
| ---------- dx = C + -----------------------------------------------
| 2 + cos(x) 3
|
/
$$\int \frac{1}{\cos{\left(x \right)} + 2}\, dx = C + \frac{2 \sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
The graph
The answer
[src]
/ / ___ \\
___ | |\/ 3 *tan(1/2)||
___ 2*\/ 3 *|-pi + atan|--------------||
2*pi*\/ 3 \ \ 3 //
---------- + ------------------------------------
3 3
$$\frac{2 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{3} + \frac{2 \sqrt{3} \pi}{3}$$
=
=
/ / ___ \\
___ | |\/ 3 *tan(1/2)||
___ 2*\/ 3 *|-pi + atan|--------------||
2*pi*\/ 3 \ \ 3 //
---------- + ------------------------------------
3 3
$$\frac{2 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{3} + \frac{2 \sqrt{3} \pi}{3}$$
2*pi*sqrt(3)/3 + 2*sqrt(3)*(-pi + atan(sqrt(3)*tan(1/2)/3))/3
The graph
Use the examples entering the upper and lower limits of integration.