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Resolución de integrales/ x^2+0/ cosx^4/ (x^2+0*x+0)*cosx^4

Integral de (x^2+0*x+0)*cosx^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                      
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 |  \x  + 0*x/*cos (x) dx
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0
∫01(x2+0x)cos⁡4(x) dx\int\limits_{0}^{1} \left(x^{2} + 0 x\right) \cos^{4}{\left(x \right)}\, dx 
Integral((x^2 + 0*x)*cos(x)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                
 |                                   3                     4            3              3    4       3    4              4             2       2       3    2       2         2    3                2    3          
 | / 2      \    4             17*cos (x)*sin(x)   15*x*sin (x)   15*sin (x)*cos(x)   x *cos (x)   x *sin (x)   17*x*cos (x)   3*x*cos (x)*sin (x)   x *cos (x)*sin (x)   3*x *sin (x)*cos(x)   5*x *cos (x)*sin(x)
 | \x  + 0*x/*cos (x) dx = C - ----------------- - ------------ - ----------------- + ---------- + ---------- + ------------ - ------------------- + ------------------ + ------------------- + -------------------
 |                                     64               64                64              8            8             64                 32                   4                     8                     8         
/
∫(x2+0x)cos⁡4(x) dx=C+x3sin⁡4(x)8+x3sin⁡2(x)cos⁡2(x)4+x3cos⁡4(x)8+3x2sin⁡3(x)cos⁡(x)8+5x2sin⁡(x)cos⁡3(x)8−15xsin⁡4(x)64−3xsin⁡2(x)cos⁡2(x)32+17xcos⁡4(x)64−15sin⁡3(x)cos⁡(x)64−17sin⁡(x)cos⁡3(x)64\int \left(x^{2} + 0 x\right) \cos^{4}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{4}{\left(x \right)}}{8} + \frac{x^{3} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{x^{3} \cos^{4}{\left(x \right)}}{8} + \frac{3 x^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{5 x^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{15 x \sin^{4}{\left(x \right)}}{64} - \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} + \frac{17 x \cos^{4}{\left(x \right)}}{64} - \frac{15 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{64} - \frac{17 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{64}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.2
Trazar el gráfico f(x)
Respuesta [src] 
       4            4           2       2           3                   3          
  7*sin (1)   25*cos (1)   5*cos (1)*sin (1)   9*sin (1)*cos(1)   23*cos (1)*sin(1)
- --------- + ---------- + ----------------- + ---------------- + -----------------
      64          64               32                 64                  64
−7sin⁡4(1)64+5sin⁡2(1)cos⁡2(1)32+25cos⁡4(1)64+9sin⁡3(1)cos⁡(1)64+23sin⁡(1)cos⁡3(1)64- \frac{7 \sin^{4}{\left(1 \right)}}{64} + \frac{5 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} + \frac{25 \cos^{4}{\left(1 \right)}}{64} + \frac{9 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{64} + \frac{23 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{64} 
=
= 
       4            4           2       2           3                   3          
  7*sin (1)   25*cos (1)   5*cos (1)*sin (1)   9*sin (1)*cos(1)   23*cos (1)*sin(1)
- --------- + ---------- + ----------------- + ---------------- + -----------------
      64          64               32                 64                  64
−7sin⁡4(1)64+5sin⁡2(1)cos⁡2(1)32+25cos⁡4(1)64+9sin⁡3(1)cos⁡(1)64+23sin⁡(1)cos⁡3(1)64- \frac{7 \sin^{4}{\left(1 \right)}}{64} + \frac{5 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} + \frac{25 \cos^{4}{\left(1 \right)}}{64} + \frac{9 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{64} + \frac{23 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{64} 
-7*sin(1)^4/64 + 25*cos(1)^4/64 + 5*cos(1)^2*sin(1)^2/32 + 9*sin(1)^3*cos(1)/64 + 23*cos(1)^3*sin(1)/64
Respuesta numérica [src] 
0.103718469409355
0.103718469409355

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

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