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Resolución de integrales/ sin^2/ cos^4/ cos^4(x)sin^2(x)x

Integral de cos^4(x)sin^2(x)x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |     4       2        
 |  cos (x)*sin (x)*x dx
 |                      
/                       
0
∫01xsin⁡2(x)cos⁡4(x) dx\int\limits_{0}^{1} x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx 
Integral((cos(x)^4*sin(x)^2)*x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                
 |                               6         6         4       2       2    6       2    6           5                  3       3           5                2    2       4         2    4       2   
 |    4       2               sin (x)   cos (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)
 | cos (x)*sin (x)*x dx = C - ------- + ------- + --------------- + ---------- + ---------- - ---------------- + ----------------- + ---------------- + -------------------- + --------------------
 |                               96       288            24             32           32              16                  6                  16                   32                     32         
/
∫xsin⁡2(x)cos⁡4(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)96+sin⁡2(x)cos⁡4(x)24+cos⁡6(x)288\int x \sin^{2}{\left(x \right)} \cos^{4}{\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)}}{96} + \frac{\sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{24} + \frac{\cos^{6}{\left(x \right)}}{288}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.2
Trazar el gráfico f(x)
Respuesta [src] 
           6           6         5                3       3         5                  2       4            4       2   
   1    sin (1)   5*cos (1)   cos (1)*sin(1)   cos (1)*sin (1)   sin (1)*cos(1)   3*cos (1)*sin (1)   13*cos (1)*sin (1)
- --- + ------- + --------- - -------------- + --------------- + -------------- + ----------------- + ------------------
  288      48        144            16                6                16                 32                  96
−1288−sin⁡(1)cos⁡5(1)16+5cos⁡6(1)144+sin⁡6(1)48+13sin⁡2(1)cos⁡4(1)96+3sin⁡4(1)cos⁡2(1)32+sin⁡5(1)cos⁡(1)16+sin⁡3(1)cos⁡3(1)6- \frac{1}{288} - \frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{16} + \frac{5 \cos^{6}{\left(1 \right)}}{144} + \frac{\sin^{6}{\left(1 \right)}}{48} + \frac{13 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{96} + \frac{3 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} + \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{\sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{6} 
=
= 
           6           6         5                3       3         5                  2       4            4       2   
   1    sin (1)   5*cos (1)   cos (1)*sin(1)   cos (1)*sin (1)   sin (1)*cos(1)   3*cos (1)*sin (1)   13*cos (1)*sin (1)
- --- + ------- + --------- - -------------- + --------------- + -------------- + ----------------- + ------------------
  288      48        144            16                6                16                 32                  96
−1288−sin⁡(1)cos⁡5(1)16+5cos⁡6(1)144+sin⁡6(1)48+13sin⁡2(1)cos⁡4(1)96+3sin⁡4(1)cos⁡2(1)32+sin⁡5(1)cos⁡(1)16+sin⁡3(1)cos⁡3(1)6- \frac{1}{288} - \frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{16} + \frac{5 \cos^{6}{\left(1 \right)}}{144} + \frac{\sin^{6}{\left(1 \right)}}{48} + \frac{13 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{96} + \frac{3 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} + \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{\sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{6} 
-1/288 + sin(1)^6/48 + 5*cos(1)^6/144 - cos(1)^5*sin(1)/16 + cos(1)^3*sin(1)^3/6 + sin(1)^5*cos(1)/16 + 3*cos(1)^2*sin(1)^4/32 + 13*cos(1)^4*sin(1)^2/96
Respuesta numérica [src] 
0.0541685729738803
0.0541685729738803

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

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