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Integral de dx/(3cosx+2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  3*cos(x) + 2   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{1}{3 \cos{\left(x \right)} + 2}\, dx$$
Integral(1/(3*cos(x) + 2), (x, 0, 1))
Respuesta (Indefinida) [src]
  /                        ___    /    ___      /x\\     ___    /  ___      /x\\
 |                       \/ 5 *log|- \/ 5  + tan|-||   \/ 5 *log|\/ 5  + tan|-||
 |      1                         \             \2//            \           \2//
 | ------------ dx = C - --------------------------- + -------------------------
 | 3*cos(x) + 2                       5                            5            
 |                                                                              
/                                                                               
$$\int \frac{1}{3 \cos{\left(x \right)} + 2}\, dx = C - \frac{\sqrt{5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5} \right)}}{5} + \frac{\sqrt{5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5} \right)}}{5}$$
Gráfica
Respuesta [src]
    ___ /          /  ___           \\     ___    /  ___\     ___ /          /  ___\\     ___    /  ___           \
  \/ 5 *\pi*I + log\\/ 5  - tan(1/2)//   \/ 5 *log\\/ 5 /   \/ 5 *\pi*I + log\\/ 5 //   \/ 5 *log\\/ 5  + tan(1/2)/
- ------------------------------------ - ---------------- + ------------------------- + ---------------------------
                   5                            5                       5                            5             
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{5} + \frac{\sqrt{5} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{5}$$
=
=
    ___ /          /  ___           \\     ___    /  ___\     ___ /          /  ___\\     ___    /  ___           \
  \/ 5 *\pi*I + log\\/ 5  - tan(1/2)//   \/ 5 *log\\/ 5 /   \/ 5 *\pi*I + log\\/ 5 //   \/ 5 *log\\/ 5  + tan(1/2)/
- ------------------------------------ - ---------------- + ------------------------- + ---------------------------
                   5                            5                       5                            5             
$$- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{5} + \frac{\sqrt{5} \log{\left(\tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{5}$$
-sqrt(5)*(pi*i + log(sqrt(5) - tan(1/2)))/5 - sqrt(5)*log(sqrt(5))/5 + sqrt(5)*(pi*i + log(sqrt(5)))/5 + sqrt(5)*log(sqrt(5) + tan(1/2))/5
Respuesta numérica [src]
0.223031455608537
0.223031455608537

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.