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Resolución de integrales/ cox^4(5*x)

Integral de cox^4(5*x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |     4          
 |  cos (x)*5*x dx
 |                
/                 
0
∫015xcos⁡4(x) dx\int\limits_{0}^{1} 5 x \cos^{4}{\left(x \right)}\, dx 
Integral(cos(x)^4*(5*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                
 |                            4            4          2    4          2    4              3                 2    2       2              3          
 |    4                 15*sin (x)   25*cos (x)   15*x *cos (x)   15*x *sin (x)   15*x*sin (x)*cos(x)   15*x *cos (x)*sin (x)   25*x*cos (x)*sin(x)
 | cos (x)*5*x dx = C - ---------- + ---------- + ------------- + ------------- + ------------------- + --------------------- + -------------------
 |                          32           32             16              16                 8                      8                      8         
/
∫5xcos⁡4(x) dx=C+15x2sin⁡4(x)16+15x2sin⁡2(x)cos⁡2(x)8+15x2cos⁡4(x)16+15xsin⁡3(x)cos⁡(x)8+25xsin⁡(x)cos⁡3(x)8−15sin⁡4(x)32+25cos⁡4(x)32\int 5 x \cos^{4}{\left(x \right)}\, dx = C + \frac{15 x^{2} \sin^{4}{\left(x \right)}}{16} + \frac{15 x^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{15 x^{2} \cos^{4}{\left(x \right)}}{16} + \frac{15 x \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{25 x \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{15 \sin^{4}{\left(x \right)}}{32} + \frac{25 \cos^{4}{\left(x \right)}}{32}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
             4            4            2       2            3                   3          
  25   15*sin (1)   55*cos (1)   15*cos (1)*sin (1)   15*sin (1)*cos(1)   25*cos (1)*sin(1)
- -- + ---------- + ---------- + ------------------ + ----------------- + -----------------
  32       32           32               8                    8                   8
−2532+55cos⁡4(1)32+15sin⁡4(1)32+15sin⁡2(1)cos⁡2(1)8+25sin⁡(1)cos⁡3(1)8+15sin⁡3(1)cos⁡(1)8- \frac{25}{32} + \frac{55 \cos^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{25 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{15 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} 
=
= 
             4            4            2       2            3                   3          
  25   15*sin (1)   55*cos (1)   15*cos (1)*sin (1)   15*sin (1)*cos(1)   25*cos (1)*sin(1)
- -- + ---------- + ---------- + ------------------ + ----------------- + -----------------
  32       32           32               8                    8                   8
−2532+55cos⁡4(1)32+15sin⁡4(1)32+15sin⁡2(1)cos⁡2(1)8+25sin⁡(1)cos⁡3(1)8+15sin⁡3(1)cos⁡(1)8- \frac{25}{32} + \frac{55 \cos^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{25 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{15 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} 
-25/32 + 15*sin(1)^4/32 + 55*cos(1)^4/32 + 15*cos(1)^2*sin(1)^2/8 + 15*sin(1)^3*cos(1)/8 + 25*cos(1)^3*sin(1)/8
Respuesta numérica [src] 
1.00618416685829
1.00618416685829

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

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