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Resolución de integrales/ sin3x/ x^3sin3x^4

Integral de x^3sin3x^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
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 |   3    4        
 |  x *sin (3*x) dx
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/                  
0
∫01x3sin⁡4(3x) dx\int\limits_{0}^{1} x^{3} \sin^{4}{\left(3 x \right)}\, dx 
Integral(x^3*sin(3*x)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                              
 |                             4             4           2    4           4    4           4    4            2    4           3    3                  3    3                  2    2         2           4    2         2               3                         3              
 |  3    4               17*sin (3*x)   5*cos (3*x)   5*x *cos (3*x)   3*x *cos (3*x)   3*x *sin (3*x)   17*x *sin (3*x)   5*x *sin (3*x)*cos(3*x)   x *cos (3*x)*sin(3*x)   x *cos (3*x)*sin (3*x)   3*x *cos (3*x)*sin (3*x)   5*x*cos (3*x)*sin(3*x)   17*x*sin (3*x)*cos(3*x)
 | x *sin (3*x) dx = C - ------------ + ----------- - -------------- + -------------- + -------------- + --------------- - ----------------------- - --------------------- - ---------------------- + ------------------------ + ---------------------- + -----------------------
 |                           6912           2304           128               32               32               384                    24                       8                       64                        16                       192                       576          
/
∫x3sin⁡4(3x) dx=C+3x4sin⁡4(3x)32+3x4sin⁡2(3x)cos⁡2(3x)16+3x4cos⁡4(3x)32−5x3sin⁡3(3x)cos⁡(3x)24−x3sin⁡(3x)cos⁡3(3x)8+17x2sin⁡4(3x)384−x2sin⁡2(3x)cos⁡2(3x)64−5x2cos⁡4(3x)128+17xsin⁡3(3x)cos⁡(3x)576+5xsin⁡(3x)cos⁡3(3x)192−17sin⁡4(3x)6912+5cos⁡4(3x)2304\int x^{3} \sin^{4}{\left(3 x \right)}\, dx = C + \frac{3 x^{4} \sin^{4}{\left(3 x \right)}}{32} + \frac{3 x^{4} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{16} + \frac{3 x^{4} \cos^{4}{\left(3 x \right)}}{32} - \frac{5 x^{3} \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)}}{24} - \frac{x^{3} \sin{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{8} + \frac{17 x^{2} \sin^{4}{\left(3 x \right)}}{384} - \frac{x^{2} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{64} - \frac{5 x^{2} \cos^{4}{\left(3 x \right)}}{128} + \frac{17 x \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)}}{576} + \frac{5 x \sin{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{192} - \frac{17 \sin^{4}{\left(3 x \right)}}{6912} + \frac{5 \cos^{4}{\left(3 x \right)}}{2304}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.4
Trazar el gráfico f(x)
Respuesta [src] 
                4             4             3                   3                   2       2   
   5     131*cos (3)   937*sin (3)   103*sin (3)*cos(3)   19*cos (3)*sin(3)   11*cos (3)*sin (3)
- ---- + ----------- + ----------- - ------------------ - ----------------- + ------------------
  2304       2304          6912             576                  192                  64
−52304+937sin⁡4(3)6912−103sin⁡3(3)cos⁡(3)576+11sin⁡2(3)cos⁡2(3)64−19sin⁡(3)cos⁡3(3)192+131cos⁡4(3)2304- \frac{5}{2304} + \frac{937 \sin^{4}{\left(3 \right)}}{6912} - \frac{103 \sin^{3}{\left(3 \right)} \cos{\left(3 \right)}}{576} + \frac{11 \sin^{2}{\left(3 \right)} \cos^{2}{\left(3 \right)}}{64} - \frac{19 \sin{\left(3 \right)} \cos^{3}{\left(3 \right)}}{192} + \frac{131 \cos^{4}{\left(3 \right)}}{2304} 
=
= 
                4             4             3                   3                   2       2   
   5     131*cos (3)   937*sin (3)   103*sin (3)*cos(3)   19*cos (3)*sin(3)   11*cos (3)*sin (3)
- ---- + ----------- + ----------- - ------------------ - ----------------- + ------------------
  2304       2304          6912             576                  192                  64
−52304+937sin⁡4(3)6912−103sin⁡3(3)cos⁡(3)576+11sin⁡2(3)cos⁡2(3)64−19sin⁡(3)cos⁡3(3)192+131cos⁡4(3)2304- \frac{5}{2304} + \frac{937 \sin^{4}{\left(3 \right)}}{6912} - \frac{103 \sin^{3}{\left(3 \right)} \cos{\left(3 \right)}}{576} + \frac{11 \sin^{2}{\left(3 \right)} \cos^{2}{\left(3 \right)}}{64} - \frac{19 \sin{\left(3 \right)} \cos^{3}{\left(3 \right)}}{192} + \frac{131 \cos^{4}{\left(3 \right)}}{2304} 
-5/2304 + 131*cos(3)^4/2304 + 937*sin(3)^4/6912 - 103*sin(3)^3*cos(3)/576 - 19*cos(3)^3*sin(3)/192 + 11*cos(3)^2*sin(3)^2/64
Respuesta numérica [src] 
0.0699013306701471
0.0699013306701471

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