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Resolución de integrales/ sen(x)/ 1/(sen(x)+3)

Integral de 1/(sen(x)+3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |      1        
 |  ---------- dx
 |  sin(x) + 3   
 |               
/                
0
∫011sin⁡(x)+3 dx\int\limits_{0}^{1} \frac{1}{\sin{\left(x \right)} + 3}\, dx 
Integral(1/(sin(x) + 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                             /        /x   pi\       /            ___    /x\\\
                             |        |- - --|       |  ___   3*\/ 2 *tan|-|||
  /                      ___ |        |2   2 |       |\/ 2               \2/||
 |                     \/ 2 *|pi*floor|------| + atan|----- + --------------||
 |     1                     \        \  pi  /       \  4           4       //
 | ---------- dx = C + -------------------------------------------------------
 | sin(x) + 3                                     2                           
 |                                                                            
/
∫1sin⁡(x)+3 dx=C+2(atan⁡(32tan⁡(x2)4+24)+π⌊x2−π2π⌋)2\int \frac{1}{\sin{\left(x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Trazar el gráfico f(x)
Respuesta [src] 
      /          /  ___       ___         \\         /          /  ___\\
  ___ |          |\/ 2    3*\/ 2 *tan(1/2)||     ___ |          |\/ 2 ||
\/ 2 *|-pi + atan|----- + ----------------||   \/ 2 *|-pi + atan|-----||
      \          \  4            4        //         \          \  4  //
-------------------------------------------- - -------------------------
                     2                                     2
2(−π+atan⁡(24+32tan⁡(12)4))2−2(−π+atan⁡(24))2\frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right)}{2} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{2} 
=
= 
      /          /  ___       ___         \\         /          /  ___\\
  ___ |          |\/ 2    3*\/ 2 *tan(1/2)||     ___ |          |\/ 2 ||
\/ 2 *|-pi + atan|----- + ----------------||   \/ 2 *|-pi + atan|-----||
      \          \  4            4        //         \          \  4  //
-------------------------------------------- - -------------------------
                     2                                     2
2(−π+atan⁡(24+32tan⁡(12)4))2−2(−π+atan⁡(24))2\frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right)}{2} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{2} 
sqrt(2)*(-pi + atan(sqrt(2)/4 + 3*sqrt(2)*tan(1/2)/4))/2 - sqrt(2)*(-pi + atan(sqrt(2)/4))/2
Respuesta numérica [src] 
0.290558049062055
0.290558049062055

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

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