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Resolución de integrales/ cosx^2/ xcosx/ sin^3/ sin(x)/ xsin^3xcosx^2*sin(x)

Integral de xsin^3xcosx^2*sin(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
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 |       3       2             
 |  x*sin (x)*cos (x)*sin(x) dx
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0
∫01xsin⁡3(x)cos⁡2(x)sin⁡(x) dx\int\limits_{0}^{1} x \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)} \sin{\left(x \right)}\, dx 
Integral(((x*sin(x)^3)*cos(x)^2)*sin(x), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                       
 |                                      6         6         2       4       2    6       2    6           3       3           5                  5                2    2       4         2    4       2   
 |      3       2                    cos (x)   sin (x)   cos (x)*sin (x)   x *cos (x)   x *sin (x)   x*cos (x)*sin (x)   x*cos (x)*sin(x)   x*sin (x)*cos(x)   3*x *cos (x)*sin (x)   3*x *cos (x)*sin (x)
 | x*sin (x)*cos (x)*sin(x) dx = C - ------- + ------- + --------------- + ---------- + ---------- - ----------------- - ---------------- + ---------------- + -------------------- + --------------------
 |                                      96       288            24             32           32               6                  16                 16                   32                     32         
/
∫xsin⁡3(x)cos⁡2(x)sin⁡(x) dx=C+x2sin⁡6(x)32+3x2sin⁡4(x)cos⁡2(x)32+3x2sin⁡2(x)cos⁡4(x)32+x2cos⁡6(x)32+xsin⁡5(x)cos⁡(x)16−xsin⁡3(x)cos⁡3(x)6−xsin⁡(x)cos⁡5(x)16+sin⁡6(x)288+sin⁡4(x)cos⁡2(x)24−cos⁡6(x)96\int x \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)} \sin{\left(x \right)}\, dx = C + \frac{x^{2} \sin^{6}{\left(x \right)}}{32} + \frac{3 x^{2} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} + \frac{3 x^{2} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{32} + \frac{x^{2} \cos^{6}{\left(x \right)}}{32} + \frac{x \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{16} - \frac{x \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{6} - \frac{x \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{16} + \frac{\sin^{6}{\left(x \right)}}{288} + \frac{\sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{24} - \frac{\cos^{6}{\left(x \right)}}{96}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.2-0.2
Trazar el gráfico f(x)
Respuesta [src] 
        6           6         3       3         5                5                  4       2            2       4   
1    cos (1)   5*sin (1)   cos (1)*sin (1)   cos (1)*sin(1)   sin (1)*cos(1)   3*cos (1)*sin (1)   13*cos (1)*sin (1)
-- + ------- + --------- - --------------- - -------------- + -------------- + ----------------- + ------------------
96      48        144             6                16               16                 32                  96
−sin⁡3(1)cos⁡3(1)6−sin⁡(1)cos⁡5(1)16+cos⁡6(1)48+3sin⁡2(1)cos⁡4(1)32+196+5sin⁡6(1)144+sin⁡5(1)cos⁡(1)16+13sin⁡4(1)cos⁡2(1)96- \frac{\sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{6} - \frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{16} + \frac{\cos^{6}{\left(1 \right)}}{48} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{32} + \frac{1}{96} + \frac{5 \sin^{6}{\left(1 \right)}}{144} + \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{13 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{96} 
=
= 
        6           6         3       3         5                5                  4       2            2       4   
1    cos (1)   5*sin (1)   cos (1)*sin (1)   cos (1)*sin(1)   sin (1)*cos(1)   3*cos (1)*sin (1)   13*cos (1)*sin (1)
-- + ------- + --------- - --------------- - -------------- + -------------- + ----------------- + ------------------
96      48        144             6                16               16                 32                  96
−sin⁡3(1)cos⁡3(1)6−sin⁡(1)cos⁡5(1)16+cos⁡6(1)48+3sin⁡2(1)cos⁡4(1)32+196+5sin⁡6(1)144+sin⁡5(1)cos⁡(1)16+13sin⁡4(1)cos⁡2(1)96- \frac{\sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{6} - \frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{16} + \frac{\cos^{6}{\left(1 \right)}}{48} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{32} + \frac{1}{96} + \frac{5 \sin^{6}{\left(1 \right)}}{144} + \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{13 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{96} 
1/96 + cos(1)^6/48 + 5*sin(1)^6/144 - cos(1)^3*sin(1)^3/6 - cos(1)^5*sin(1)/16 + sin(1)^5*cos(1)/16 + 3*cos(1)^4*sin(1)^2/32 + 13*cos(1)^2*sin(1)^4/96
Respuesta numérica [src] 
0.0449005957924894
0.0449005957924894

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

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