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Resolución de integrales/ cos^6/ (cos^6)(4x)

Integral de (cos^6)(4x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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 |     6          
 |  cos (x)*4*x dx
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0
∫014xcos⁡6(x) dx\int\limits_{0}^{1} 4 x \cos^{6}{\left(x \right)}\, dx 
Integral(cos(x)^6*(4*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   
 |    6                 5*sin (x)   53*cos (x)   5*cos (x)*sin (x)   5*x *cos (x)   5*x *sin (x)   5*x*sin (x)*cos(x)   10*x*cos (x)*sin (x)   11*x*cos (x)*sin(x)   15*x *cos (x)*sin (x)   15*x *cos (x)*sin (x)
 | cos (x)*4*x dx = C - --------- + ---------- + ----------------- + ------------ + ------------ + ------------------ + -------------------- + ------------------- + --------------------- + ---------------------
 |                          24          72               6                8              8                 4                     3                      4                      8                       8          
/
∫4xcos⁡6(x) dx=C+5x2sin⁡6(x)8+15x2sin⁡4(x)cos⁡2(x)8+15x2sin⁡2(x)cos⁡4(x)8+5x2cos⁡6(x)8+5xsin⁡5(x)cos⁡(x)4+10xsin⁡3(x)cos⁡3(x)3+11xsin⁡(x)cos⁡5(x)4−5sin⁡6(x)24+5sin⁡2(x)cos⁡4(x)6+53cos⁡6(x)72\int 4 x \cos^{6}{\left(x \right)}\, dx = C + \frac{5 x^{2} \sin^{6}{\left(x \right)}}{8} + \frac{15 x^{2} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{15 x^{2} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{8} + \frac{5 x^{2} \cos^{6}{\left(x \right)}}{8} + \frac{5 x \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{10 x \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} + \frac{11 x \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{4} - \frac{5 \sin^{6}{\left(x \right)}}{24} + \frac{5 \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{6} + \frac{53 \cos^{6}{\left(x \right)}}{72}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
            6            6           5                   3       3            5                   2       4            4       2   
  53   5*sin (1)   49*cos (1)   5*sin (1)*cos(1)   10*cos (1)*sin (1)   11*cos (1)*sin(1)   15*cos (1)*sin (1)   65*cos (1)*sin (1)
- -- + --------- + ---------- + ---------------- + ------------------ + ----------------- + ------------------ + ------------------
  72       12          36              4                   3                    4                   8                    24
−5372+49cos⁡6(1)36+11sin⁡(1)cos⁡5(1)4+5sin⁡6(1)12+65sin⁡2(1)cos⁡4(1)24+15sin⁡4(1)cos⁡2(1)8+5sin⁡5(1)cos⁡(1)4+10sin⁡3(1)cos⁡3(1)3- \frac{53}{72} + \frac{49 \cos^{6}{\left(1 \right)}}{36} + \frac{11 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{4} + \frac{5 \sin^{6}{\left(1 \right)}}{12} + \frac{65 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{24} + \frac{15 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{5 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{4} + \frac{10 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3} 
=
= 
            6            6           5                   3       3            5                   2       4            4       2   
  53   5*sin (1)   49*cos (1)   5*sin (1)*cos(1)   10*cos (1)*sin (1)   11*cos (1)*sin(1)   15*cos (1)*sin (1)   65*cos (1)*sin (1)
- -- + --------- + ---------- + ---------------- + ------------------ + ----------------- + ------------------ + ------------------
  72       12          36              4                   3                    4                   8                    24
−5372+49cos⁡6(1)36+11sin⁡(1)cos⁡5(1)4+5sin⁡6(1)12+65sin⁡2(1)cos⁡4(1)24+15sin⁡4(1)cos⁡2(1)8+5sin⁡5(1)cos⁡(1)4+10sin⁡3(1)cos⁡3(1)3- \frac{53}{72} + \frac{49 \cos^{6}{\left(1 \right)}}{36} + \frac{11 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{4} + \frac{5 \sin^{6}{\left(1 \right)}}{12} + \frac{65 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{24} + \frac{15 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{5 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{4} + \frac{10 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3} 
-53/72 + 5*sin(1)^6/12 + 49*cos(1)^6/36 + 5*sin(1)^5*cos(1)/4 + 10*cos(1)^3*sin(1)^3/3 + 11*cos(1)^5*sin(1)/4 + 15*cos(1)^2*sin(1)^4/8 + 65*cos(1)^4*sin(1)^2/24
Respuesta numérica [src] 
0.58827304159111
0.58827304159111

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

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