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Resolución de integrales/ sin3x/ (1)/(sin3x+5)

Integral de (1)/(sin3x+5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  sin(3*x) + 5   
 |                 
/                  
0
∫011sin⁡(3x)+5 dx\int\limits_{0}^{1} \frac{1}{\sin{\left(3 x \right)} + 5}\, dx 
Integral(1/(sin(3*x) + 5), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               /        /  pi   3*x\       /            ___    /3*x\\\
                               |        |- -- + ---|       |  ___   5*\/ 6 *tan|---|||
  /                        ___ |        |  2     2 |       |\/ 6               \ 2 /||
 |                       \/ 6 *|pi*floor|----------| + atan|----- + ----------------||
 |      1                      \        \    pi    /       \  12           12       //
 | ------------ dx = C + -------------------------------------------------------------
 | sin(3*x) + 5                                        18                             
 |                                                                                    
/
∫1sin⁡(3x)+5 dx=C+6(atan⁡(56tan⁡(3x2)12+612)+π⌊3x2−π2π⌋)18\int \frac{1}{\sin{\left(3 x \right)} + 5}\, dx = C + \frac{\sqrt{6} \left(\operatorname{atan}{\left(\frac{5 \sqrt{6} \tan{\left(\frac{3 x}{2} \right)}}{12} + \frac{\sqrt{6}}{12} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{18}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Trazar el gráfico f(x)
Respuesta [src] 
        /          /  ___\\         /          /  ___       ___         \\
    ___ |          |\/ 6 ||     ___ |          |\/ 6    5*\/ 6 *tan(3/2)||
  \/ 6 *|-pi + atan|-----||   \/ 6 *|-pi + atan|----- + ----------------||
        \          \  12 //         \          \  12           12       //
- ------------------------- + --------------------------------------------
              18                                   18
6(−π+atan⁡(612+56tan⁡(32)12))18−6(−π+atan⁡(612))18\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6} \tan{\left(\frac{3}{2} \right)}}{12} \right)}\right)}{18} - \frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} \right)}\right)}{18} 
=
= 
        /          /  ___\\         /          /  ___       ___         \\
    ___ |          |\/ 6 ||     ___ |          |\/ 6    5*\/ 6 *tan(3/2)||
  \/ 6 *|-pi + atan|-----||   \/ 6 *|-pi + atan|----- + ----------------||
        \          \  12 //         \          \  12           12       //
- ------------------------- + --------------------------------------------
              18                                   18
6(−π+atan⁡(612+56tan⁡(32)12))18−6(−π+atan⁡(612))18\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6} \tan{\left(\frac{3}{2} \right)}}{12} \right)}\right)}{18} - \frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} \right)}\right)}{18} 
-sqrt(6)*(-pi + atan(sqrt(6)/12))/18 + sqrt(6)*(-pi + atan(sqrt(6)/12 + 5*sqrt(6)*tan(3/2)/12))/18
Respuesta numérica [src] 
0.177048424709258
0.177048424709258

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

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