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Resolución de integrales/ sin^6/ cos^2/ 2^4*sin^6(x)cos^2x

Integral de 2^4*sin^6(x)cos^2x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  x                      
  /                      
 |                       
 |        6       2      
 |  16*sin (x)*cos (x) dx
 |                       
/                        
0
$$\int\limits_{0}^{x} 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral((16*sin(x)^6)*cos(x)^2, (x, 0, x))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                        
 |                                   3       5            5       3           7                    8             8           7                    2       6             6       2              4       4   
 |       6       2             73*cos (x)*sin (x)   55*cos (x)*sin (x)   5*cos (x)*sin(x)   5*x*cos (x)   5*x*sin (x)   5*sin (x)*cos(x)   5*x*cos (x)*sin (x)   5*x*cos (x)*sin (x)   15*x*cos (x)*sin (x)
 | 16*sin (x)*cos (x) dx = C - ------------------ - ------------------ - ---------------- + ----------- + ----------- + ---------------- + ------------------- + ------------------- + --------------------
 |                                     24                   24                  8                8             8               8                    2                     2                     4          
/
$$\int 16 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + \frac{5 x \sin^{8}{\left(x \right)}}{8} + \frac{5 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{15 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{5 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{5 x \cos^{8}{\left(x \right)}}{8} + \frac{5 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{73 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{24} - \frac{55 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{24} - \frac{5 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}$$
Simplificar
Respuesta [src] 
                                                3                5          
5*x        7             5*cos(x)*sin(x)   5*sin (x)*cos(x)   sin (x)*cos(x)
--- + 2*sin (x)*cos(x) - --------------- - ---------------- - --------------
 8                              8                 12                3
$$\frac{5 x}{8} + 2 \sin^{7}{\left(x \right)} \cos{\left(x \right)} - \frac{\sin^{5}{\left(x \right)} \cos{\left(x \right)}}{3} - \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{12} - \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{8}$$ 
=
= 
                                                3                5          
5*x        7             5*cos(x)*sin(x)   5*sin (x)*cos(x)   sin (x)*cos(x)
--- + 2*sin (x)*cos(x) - --------------- - ---------------- - --------------
 8                              8                 12                3
$$\frac{5 x}{8} + 2 \sin^{7}{\left(x \right)} \cos{\left(x \right)} - \frac{\sin^{5}{\left(x \right)} \cos{\left(x \right)}}{3} - \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{12} - \frac{5 \sin{\left(x \right)} \cos{\left(x \right)}}{8}$$ 
5*x/8 + 2*sin(x)^7*cos(x) - 5*cos(x)*sin(x)/8 - 5*sin(x)^3*cos(x)/12 - sin(x)^5*cos(x)/3

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

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