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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/5x
- Integral of sqrt(1+e^(2x))
- Integral of sinx/cos2x
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Integral of sqrt(1-x^2)dx
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Identical expressions
- (one /(three + two *cos(3x)))
- (1 divide by (3 plus 2 multiply by co sinus of e of (3x)))
- (one divide by (three plus two multiply by co sinus of e of (3x)))
- (1/(3+2cos(3x)))
- 1/3+2cos3x
- (1 divide by (3+2*cos(3x)))
- (1/(3+2*cos(3x)))dx
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Similar expressions
- 1/(3+2cos(3x)-sin(3x))
- (1/(3-2*cos(3x)))
Integral of (1/(3+2*cos(3x))) dx
The solution
You have entered
[src]
pi -- 3 / | | 1 | -------------- dx | 3 + 2*cos(3*x) | / 0
$$\int\limits_{0}^{\frac{\pi}{3}} \frac{1}{2 \cos{\left(3 x \right)} + 3}\, dx$$
Integral(1/(3 + 2*cos(3*x)), (x, 0, pi/3))
The answer (Indefinite)
[src]
/ / pi 3*x\ / ___ /3*x\\\
| |- -- + ---| |\/ 5 *tan|---|||
/ ___ | | 2 2 | | \ 2 /||
| 2*\/ 5 *|pi*floor|----------| + atan|--------------||
| 1 \ \ pi / \ 5 //
| -------------- dx = C + -----------------------------------------------------
| 3 + 2*cos(3*x) 15
|
/
$$\int \frac{1}{2 \cos{\left(3 x \right)} + 3}\, dx = C + \frac{2 \sqrt{5} \left(\operatorname{atan}{\left(\frac{\sqrt{5} \tan{\left(\frac{3 x}{2} \right)}}{5} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{15}$$
The graph
The answer
[src]
___ pi*\/ 5 -------- 15
$$\frac{\sqrt{5} \pi}{15}$$
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=
___ pi*\/ 5 -------- 15
$$\frac{\sqrt{5} \pi}{15}$$
pi*sqrt(5)/15
Use the examples entering the upper and lower limits of integration.