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Resolución de integrales/ sin(ax)/ xsin(ax)dx

Integral de xsin(ax)dx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |  x*sin(a*x) dx
 |               
/                
0
∫01xsin⁡(ax) dx\int\limits_{0}^{1} x \sin{\left(a x \right)}\, dx 
Integral(x*sin(a*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                       //            0              for a = 0\                             
                       ||                                    |                             
  /                    || //sin(a*x)            \            |     //    0       for a = 0\
 |                     || ||--------  for a != 0|            |     ||                     |
 | x*sin(a*x) dx = C - |<-|<   a                |            | + x*|<-cos(a*x)            |
 |                     || ||                    |            |     ||----------  otherwise|
/                      || \\   x      otherwise /            |     \\    a                /
                       ||-------------------------  otherwise|                             
                       \\            a                       /
∫xsin⁡(ax) dx=C+x({0for a=0−cos⁡(ax)aotherwise)−{0for a=0−{sin⁡(ax)afor a≠0xotherwiseaotherwise\int x \sin{\left(a x \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos{\left(a x \right)}}{a} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\begin{cases} \frac{\sin{\left(a x \right)}}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}}{a} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/sin(a)   cos(a)                                  
|------ - ------  for And(a > -oo, a < oo, a != 0)
|   2       a                                     
<  a                                              
|                                                 
|       0                    otherwise            
\
{−cos⁡(a)a+sin⁡(a)a2for a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{\cos{\left(a \right)}}{a} + \frac{\sin{\left(a \right)}}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
=
= 
/sin(a)   cos(a)                                  
|------ - ------  for And(a > -oo, a < oo, a != 0)
|   2       a                                     
<  a                                              
|                                                 
|       0                    otherwise            
\
{−cos⁡(a)a+sin⁡(a)a2for a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{\cos{\left(a \right)}}{a} + \frac{\sin{\left(a \right)}}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
Piecewise((sin(a)/a^2 - cos(a)/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))

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

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