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Integral de 1/(2sin(x)+5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  2*sin(x) + 5   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{1}{2 \sin{\left(x \right)} + 5}\, dx$$
Integral(1/(2*sin(x) + 5), (x, 0, 1))
Respuesta (Indefinida) [src]
                                  /        /x   pi\       /               ____    /x\\\
                                  |        |- - --|       |    ____   5*\/ 21 *tan|-|||
  /                          ____ |        |2   2 |       |2*\/ 21                \2/||
 |                       2*\/ 21 *|pi*floor|------| + atan|-------- + ---------------||
 |      1                         \        \  pi  /       \   21             21      //
 | ------------ dx = C + --------------------------------------------------------------
 | 2*sin(x) + 5                                        21                              
 |                                                                                     
/                                                                                      
$$\int \frac{1}{2 \sin{\left(x \right)} + 5}\, dx = C + \frac{2 \sqrt{21} \left(\operatorname{atan}{\left(\frac{5 \sqrt{21} \tan{\left(\frac{x}{2} \right)}}{21} + \frac{2 \sqrt{21}}{21} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{21}$$
Gráfica
Respuesta [src]
           /          /    ____\\            /          /    ____       ____         \\
      ____ |          |2*\/ 21 ||       ____ |          |2*\/ 21    5*\/ 21 *tan(1/2)||
  2*\/ 21 *|-pi + atan|--------||   2*\/ 21 *|-pi + atan|-------- + -----------------||
           \          \   21   //            \          \   21              21       //
- ------------------------------- + ---------------------------------------------------
                 21                                          21                        
$$\frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} + \frac{5 \sqrt{21} \tan{\left(\frac{1}{2} \right)}}{21} \right)}\right)}{21} - \frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}\right)}{21}$$
=
=
           /          /    ____\\            /          /    ____       ____         \\
      ____ |          |2*\/ 21 ||       ____ |          |2*\/ 21    5*\/ 21 *tan(1/2)||
  2*\/ 21 *|-pi + atan|--------||   2*\/ 21 *|-pi + atan|-------- + -----------------||
           \          \   21   //            \          \   21              21       //
- ------------------------------- + ---------------------------------------------------
                 21                                          21                        
$$\frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} + \frac{5 \sqrt{21} \tan{\left(\frac{1}{2} \right)}}{21} \right)}\right)}{21} - \frac{2 \sqrt{21} \left(- \pi + \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}\right)}{21}$$
-2*sqrt(21)*(-pi + atan(2*sqrt(21)/21))/21 + 2*sqrt(21)*(-pi + atan(2*sqrt(21)/21 + 5*sqrt(21)*tan(1/2)/21))/21
Respuesta numérica [src]
0.170153408085023
0.170153408085023

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