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Resolución de integrales/ sin(6*x)/ 1/(sin(6*x)+3)

Integral de 1/(sin(6*x)+3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  sin(6*x) + 3   
 |                 
/                  
0
∫011sin⁡(6x)+3 dx\int\limits_{0}^{1} \frac{1}{\sin{\left(6 x \right)} + 3}\, dx 
Integral(1/(sin(6*x) + 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               /        /      pi\                                 \
                               |        |3*x - --|       /  ___       ___         \|
  /                        ___ |        |      2 |       |\/ 2    3*\/ 2 *tan(3*x)||
 |                       \/ 2 *|pi*floor|--------| + atan|----- + ----------------||
 |      1                      \        \   pi   /       \  4            4        //
 | ------------ dx = C + -----------------------------------------------------------
 | sin(6*x) + 3                                       12                            
 |                                                                                  
/
∫1sin⁡(6x)+3 dx=C+2(atan⁡(32tan⁡(3x)4+24)+π⌊3x−π2π⌋)12\int \frac{1}{\sin{\left(6 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(3 x \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{3 x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{12}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901.0-1.0
Trazar el gráfico f(x)
Respuesta [src] 
        /          /  ___\\             /  ___       ___       \
    ___ |          |\/ 2 ||     ___     |\/ 2    3*\/ 2 *tan(3)|
  \/ 2 *|-pi + atan|-----||   \/ 2 *atan|----- + --------------|
        \          \  4  //             \  4           4       /
- ------------------------- + ----------------------------------
              12                              12
2atan⁡(32tan⁡(3)4+24)12−2(−π+atan⁡(24))12\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(3 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{12} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{12} 
=
= 
        /          /  ___\\             /  ___       ___       \
    ___ |          |\/ 2 ||     ___     |\/ 2    3*\/ 2 *tan(3)|
  \/ 2 *|-pi + atan|-----||   \/ 2 *atan|----- + --------------|
        \          \  4  //             \  4           4       /
- ------------------------- + ----------------------------------
              12                              12
2atan⁡(32tan⁡(3)4+24)12−2(−π+atan⁡(24))12\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(3 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{12} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{12} 
-sqrt(2)*(-pi + atan(sqrt(2)/4))/12 + sqrt(2)*atan(sqrt(2)/4 + 3*sqrt(2)*tan(3)/4)/12
Respuesta numérica [src] 
0.353720674752163
0.353720674752163

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

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