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Resolución de integrales/ cos^4/ (cos^4)*x

Integral de (cos^4)*x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
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 |              
 |     4        
 |  cos (x)*x dx
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0
∫01xcos⁡4(x) dx\int\limits_{0}^{1} x \cos^{4}{\left(x \right)}\, dx 
Integral(cos(x)^4*x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                       
 |                         4           4         2    4         2    4             3                2    2       2             3          
 |    4               3*sin (x)   5*cos (x)   3*x *cos (x)   3*x *sin (x)   3*x*sin (x)*cos(x)   3*x *cos (x)*sin (x)   5*x*cos (x)*sin(x)
 | cos (x)*x dx = C - --------- + --------- + ------------ + ------------ + ------------------ + -------------------- + ------------------
 |                        32          32           16             16                8                     8                     8         
/
∫xcos⁡4(x) dx=C+3x2sin⁡4(x)16+3x2sin⁡2(x)cos⁡2(x)8+3x2cos⁡4(x)16+3xsin⁡3(x)cos⁡(x)8+5xsin⁡(x)cos⁡3(x)8−3sin⁡4(x)32+5cos⁡4(x)32\int x \cos^{4}{\left(x \right)}\, dx = C + \frac{3 x^{2} \sin^{4}{\left(x \right)}}{16} + \frac{3 x^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{3 x^{2} \cos^{4}{\left(x \right)}}{16} + \frac{3 x \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{5 x \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{3 \sin^{4}{\left(x \right)}}{32} + \frac{5 \cos^{4}{\left(x \right)}}{32}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Trazar el gráfico f(x)
Respuesta [src] 
            4            4           2       2           3                  3          
  5    3*sin (1)   11*cos (1)   3*cos (1)*sin (1)   3*sin (1)*cos(1)   5*cos (1)*sin(1)
- -- + --------- + ---------- + ----------------- + ---------------- + ----------------
  32       32          32               8                  8                  8
−532+11cos⁡4(1)32+3sin⁡4(1)32+3sin⁡2(1)cos⁡2(1)8+5sin⁡(1)cos⁡3(1)8+3sin⁡3(1)cos⁡(1)8- \frac{5}{32} + \frac{11 \cos^{4}{\left(1 \right)}}{32} + \frac{3 \sin^{4}{\left(1 \right)}}{32} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} 
=
= 
            4            4           2       2           3                  3          
  5    3*sin (1)   11*cos (1)   3*cos (1)*sin (1)   3*sin (1)*cos(1)   5*cos (1)*sin(1)
- -- + --------- + ---------- + ----------------- + ---------------- + ----------------
  32       32          32               8                  8                  8
−532+11cos⁡4(1)32+3sin⁡4(1)32+3sin⁡2(1)cos⁡2(1)8+5sin⁡(1)cos⁡3(1)8+3sin⁡3(1)cos⁡(1)8- \frac{5}{32} + \frac{11 \cos^{4}{\left(1 \right)}}{32} + \frac{3 \sin^{4}{\left(1 \right)}}{32} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} 
-5/32 + 3*sin(1)^4/32 + 11*cos(1)^4/32 + 3*cos(1)^2*sin(1)^2/8 + 3*sin(1)^3*cos(1)/8 + 5*cos(1)^3*sin(1)/8
Respuesta numérica [src] 
0.201236833371658
0.201236833371658

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

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