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Resolución de integrales/ (x)^2/ cos(x)/ sin(x)/ cos(x)/(sin(x)^2-3)

Integral de cos(x)/(sin(x)^2-3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |     cos(x)     
 |  ----------- dx
 |     2          
 |  sin (x) - 3   
 |                
/                 
0
∫01cos⁡(x)sin⁡2(x)−3 dx\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} - 3}\, dx 
Integral(cos(x)/(sin(x)^2 - 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                            
 |                        ___    /  ___         \     ___    /    ___         \
 |    cos(x)            \/ 3 *log\\/ 3  + sin(x)/   \/ 3 *log\- \/ 3  + sin(x)/
 | ----------- dx = C - ------------------------- + ---------------------------
 |    2                             6                            6             
 | sin (x) - 3                                                                 
 |                                                                             
/
∫cos⁡(x)sin⁡2(x)−3 dx=C+3log⁡(sin⁡(x)−3)6−3log⁡(sin⁡(x)+3)6\int \frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} - 3}\, dx = C + \frac{\sqrt{3} \log{\left(\sin{\left(x \right)} - \sqrt{3} \right)}}{6} - \frac{\sqrt{3} \log{\left(\sin{\left(x \right)} + \sqrt{3} \right)}}{6}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-0.4-0.2
Trazar el gráfico f(x)
Respuesta [src] 
    ___ /          /  ___\\     ___    /  ___         \     ___ /          /  ___         \\     ___    /  ___\
  \/ 3 *\pi*I + log\\/ 3 //   \/ 3 *log\\/ 3  + sin(1)/   \/ 3 *\pi*I + log\\/ 3  - sin(1)//   \/ 3 *log\\/ 3 /
- ------------------------- - ------------------------- + ---------------------------------- + ----------------
              6                           6                               6                           6
−3log⁡(sin⁡(1)+3)6+3log⁡(3)6−3(log⁡(3)+iπ)6+3(log⁡(−sin⁡(1)+3)+iπ)6- \frac{\sqrt{3} \log{\left(\sin{\left(1 \right)} + \sqrt{3} \right)}}{6} + \frac{\sqrt{3} \log{\left(\sqrt{3} \right)}}{6} - \frac{\sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(- \sin{\left(1 \right)} + \sqrt{3} \right)} + i \pi\right)}{6} 
=
= 
    ___ /          /  ___\\     ___    /  ___         \     ___ /          /  ___         \\     ___    /  ___\
  \/ 3 *\pi*I + log\\/ 3 //   \/ 3 *log\\/ 3  + sin(1)/   \/ 3 *\pi*I + log\\/ 3  - sin(1)//   \/ 3 *log\\/ 3 /
- ------------------------- - ------------------------- + ---------------------------------- + ----------------
              6                           6                               6                           6
−3log⁡(sin⁡(1)+3)6+3log⁡(3)6−3(log⁡(3)+iπ)6+3(log⁡(−sin⁡(1)+3)+iπ)6- \frac{\sqrt{3} \log{\left(\sin{\left(1 \right)} + \sqrt{3} \right)}}{6} + \frac{\sqrt{3} \log{\left(\sqrt{3} \right)}}{6} - \frac{\sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(- \sin{\left(1 \right)} + \sqrt{3} \right)} + i \pi\right)}{6} 
-sqrt(3)*(pi*i + log(sqrt(3)))/6 - sqrt(3)*log(sqrt(3) + sin(1))/6 + sqrt(3)*(pi*i + log(sqrt(3) - sin(1)))/6 + sqrt(3)*log(sqrt(3))/6
Respuesta numérica [src] 
-0.306329885232616
-0.306329885232616

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

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