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Resolución de integrales/ cos^2/ xcos^2(x)x

Integral de xcos^2(x)x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  a               
  /               
 |                
 |       2        
 |  x*cos (x)*x dx
 |                
/                 
-a
$$\int\limits_{- a}^{a} x x \cos^{2}{\left(x \right)}\, dx$$ 
Integral((x*cos(x)^2)*x, (x, -a, a))
Respuesta (Indefinida) [src] 
  /                                                                                                       
 |                           2                           2       3    2       3    2       2              
 |      2               x*sin (x)   cos(x)*sin(x)   x*cos (x)   x *cos (x)   x *sin (x)   x *cos(x)*sin(x)
 | x*cos (x)*x dx = C - --------- - ------------- + --------- + ---------- + ---------- + ----------------
 |                          4             4             4           6            6               2        
/
$$\int x x \cos^{2}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} + \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{x \sin^{2}{\left(x \right)}}{4} + \frac{x \cos^{2}{\left(x \right)}}{4} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}$$
Simplificar
Respuesta [src] 
     2           2                       3    2       3    2                      
a*cos (a)   a*sin (a)   cos(a)*sin(a)   a *cos (a)   a *sin (a)    2              
--------- - --------- - ------------- + ---------- + ---------- + a *cos(a)*sin(a)
    2           2             2             3            3
$$\frac{a^{3} \sin^{2}{\left(a \right)}}{3} + \frac{a^{3} \cos^{2}{\left(a \right)}}{3} + a^{2} \sin{\left(a \right)} \cos{\left(a \right)} - \frac{a \sin^{2}{\left(a \right)}}{2} + \frac{a \cos^{2}{\left(a \right)}}{2} - \frac{\sin{\left(a \right)} \cos{\left(a \right)}}{2}$$ 
=
= 
     2           2                       3    2       3    2                      
a*cos (a)   a*sin (a)   cos(a)*sin(a)   a *cos (a)   a *sin (a)    2              
--------- - --------- - ------------- + ---------- + ---------- + a *cos(a)*sin(a)
    2           2             2             3            3
$$\frac{a^{3} \sin^{2}{\left(a \right)}}{3} + \frac{a^{3} \cos^{2}{\left(a \right)}}{3} + a^{2} \sin{\left(a \right)} \cos{\left(a \right)} - \frac{a \sin^{2}{\left(a \right)}}{2} + \frac{a \cos^{2}{\left(a \right)}}{2} - \frac{\sin{\left(a \right)} \cos{\left(a \right)}}{2}$$ 
a*cos(a)^2/2 - a*sin(a)^2/2 - cos(a)*sin(a)/2 + a^3*cos(a)^2/3 + a^3*sin(a)^2/3 + a^2*cos(a)*sin(a)

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

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