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Resolución de integrales/ 4cosx/ 1/(1+4cosx)

Integral de 1/(1+4cosx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  1 + 4*cos(x)   
 |                 
/                  
0
∫0114cos⁡(x)+1 dx\int\limits_{0}^{1} \frac{1}{4 \cos{\left(x \right)} + 1}\, dx 
Integral(1/(1 + 4*cos(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                   /    ____         \             /  ____         \
  /                        ____    |  \/ 15       /x\|     ____    |\/ 15       /x\|
 |                       \/ 15 *log|- ------ + tan|-||   \/ 15 *log|------ + tan|-||
 |      1                          \    3         \2//             \  3         \2//
 | ------------ dx = C - ----------------------------- + ---------------------------
 | 1 + 4*cos(x)                        15                             15            
 |                                                                                  
/
∫14cos⁡(x)+1 dx=C−15log⁡(tan⁡(x2)−153)15+15log⁡(tan⁡(x2)+153)15\int \frac{1}{4 \cos{\left(x \right)} + 1}\, dx = C - \frac{\sqrt{15} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{15}}{3} \right)}}{15} + \frac{\sqrt{15} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{15}}{3} \right)}}{15}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.10.4
Trazar el gráfico f(x)
Respuesta [src] 
         /          /              ____\\             /  ____\          /          /  ____\\             /  ____           \
    ____ |          |            \/ 15 ||     ____    |\/ 15 |     ____ |          |\/ 15 ||     ____    |\/ 15            |
  \/ 15 *|pi*I + log|-tan(1/2) + ------||   \/ 15 *log|------|   \/ 15 *|pi*I + log|------||   \/ 15 *log|------ + tan(1/2)|
         \          \              3   //             \  3   /          \          \  3   //             \  3              /
- --------------------------------------- - ------------------ + --------------------------- + -----------------------------
                     15                             15                        15                             15
−15log⁡(153)15+15log⁡(tan⁡(12)+153)15−15(log⁡(−tan⁡(12)+153)+iπ)15+15(log⁡(153)+iπ)15- \frac{\sqrt{15} \log{\left(\frac{\sqrt{15}}{3} \right)}}{15} + \frac{\sqrt{15} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{15}}{3} \right)}}{15} - \frac{\sqrt{15} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{15}}{3} \right)} + i \pi\right)}{15} + \frac{\sqrt{15} \left(\log{\left(\frac{\sqrt{15}}{3} \right)} + i \pi\right)}{15} 
=
= 
         /          /              ____\\             /  ____\          /          /  ____\\             /  ____           \
    ____ |          |            \/ 15 ||     ____    |\/ 15 |     ____ |          |\/ 15 ||     ____    |\/ 15            |
  \/ 15 *|pi*I + log|-tan(1/2) + ------||   \/ 15 *log|------|   \/ 15 *|pi*I + log|------||   \/ 15 *log|------ + tan(1/2)|
         \          \              3   //             \  3   /          \          \  3   //             \  3              /
- --------------------------------------- - ------------------ + --------------------------- + -----------------------------
                     15                             15                        15                             15
−15log⁡(153)15+15log⁡(tan⁡(12)+153)15−15(log⁡(−tan⁡(12)+153)+iπ)15+15(log⁡(153)+iπ)15- \frac{\sqrt{15} \log{\left(\frac{\sqrt{15}}{3} \right)}}{15} + \frac{\sqrt{15} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{15}}{3} \right)}}{15} - \frac{\sqrt{15} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{15}}{3} \right)} + i \pi\right)}{15} + \frac{\sqrt{15} \left(\log{\left(\frac{\sqrt{15}}{3} \right)} + i \pi\right)}{15} 
-sqrt(15)*(pi*i + log(-tan(1/2) + sqrt(15)/3))/15 - sqrt(15)*log(sqrt(15)/3)/15 + sqrt(15)*(pi*i + log(sqrt(15)/3))/15 + sqrt(15)*log(sqrt(15)/3 + tan(1/2))/15
Respuesta numérica [src] 
0.233174268970579
0.233174268970579

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

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