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Resolución de integrales/ sin*3*x/ 3*x^3/ x^2*sin*3*x^3

Integral de x^2*sin*3*x^3 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |   2    3        
 |  x *sin (3*x) dx
 |                 
/                  
0
∫01x2sin⁡3(3x) dx\int\limits_{0}^{1} x^{2} \sin^{3}{\left(3 x \right)}\, dx 
Integral(x^2*sin(3*x)^3, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                             
 |                             3           2    3                3              2                  2    2                        2              
 |  2    3               40*cos (3*x)   2*x *cos (3*x)   14*x*sin (3*x)   14*sin (3*x)*cos(3*x)   x *sin (3*x)*cos(3*x)   4*x*cos (3*x)*sin(3*x)
 | x *sin (3*x) dx = C + ------------ - -------------- + -------------- + --------------------- - --------------------- + ----------------------
 |                           729              9                81                  243                      3                       27          
/
∫x2sin⁡3(3x) dx=C−x2sin⁡2(3x)cos⁡(3x)3−2x2cos⁡3(3x)9+14xsin⁡3(3x)81+4xsin⁡(3x)cos⁡2(3x)27+14sin⁡2(3x)cos⁡(3x)243+40cos⁡3(3x)729\int x^{2} \sin^{3}{\left(3 x \right)}\, dx = C - \frac{x^{2} \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{3} - \frac{2 x^{2} \cos^{3}{\left(3 x \right)}}{9} + \frac{14 x \sin^{3}{\left(3 x \right)}}{81} + \frac{4 x \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{27} + \frac{14 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{243} + \frac{40 \cos^{3}{\left(3 x \right)}}{729}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Trazar el gráfico f(x)
Respuesta [src] 
               3            3            2                  2          
   40   122*cos (3)   14*sin (3)   67*sin (3)*cos(3)   4*cos (3)*sin(3)
- --- - ----------- + ---------- - ----------------- + ----------------
  729       729           81              243                 27
−40729+14sin⁡3(3)81−67sin⁡2(3)cos⁡(3)243+4sin⁡(3)cos⁡2(3)27−122cos⁡3(3)729- \frac{40}{729} + \frac{14 \sin^{3}{\left(3 \right)}}{81} - \frac{67 \sin^{2}{\left(3 \right)} \cos{\left(3 \right)}}{243} + \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(3 \right)}}{27} - \frac{122 \cos^{3}{\left(3 \right)}}{729} 
=
= 
               3            3            2                  2          
   40   122*cos (3)   14*sin (3)   67*sin (3)*cos(3)   4*cos (3)*sin(3)
- --- - ----------- + ---------- - ----------------- + ----------------
  729       729           81              243                 27
−40729+14sin⁡3(3)81−67sin⁡2(3)cos⁡(3)243+4sin⁡(3)cos⁡2(3)27−122cos⁡3(3)729- \frac{40}{729} + \frac{14 \sin^{3}{\left(3 \right)}}{81} - \frac{67 \sin^{2}{\left(3 \right)} \cos{\left(3 \right)}}{243} + \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(3 \right)}}{27} - \frac{122 \cos^{3}{\left(3 \right)}}{729} 
-40/729 - 122*cos(3)^3/729 + 14*sin(3)^3/81 - 67*sin(3)^2*cos(3)/243 + 4*cos(3)^2*sin(3)/27
Respuesta numérica [src] 
0.133920660516566
0.133920660516566

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

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