Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of (-1+u)/(1+u^2)
-
Integral of cos2xsinx
- Integral of √(1-cos(x))
-
Integral of 1/(1+x^(1/2))
-
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
-
Similar expressions
- (1/(3-2*cos(3x)))
- 1/(3+2cos(3x)-sin(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
$$\frac{\sqrt{5} \pi}{15}$$
=
=
___ pi*\/ 5 -------- 15
$$\frac{\sqrt{5} \pi}{15}$$
pi*sqrt(5)/15
Use the examples entering the upper and lower limits of integration.