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Resolución de integrales/ x^2*a/ x^2*a^x*dx

Integral de x^2*a^x*dx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1         
  /         
 |          
 |   2  x   
 |  x *a  dx
 |          
/           
0
∫01axx2 dx\int\limits_{0}^{1} a^{x} x^{2}\, dx 
Integral(x^2*a^x, (x, 0, 1))
Respuesta (Indefinida) [src] 
                  // x /     2    2                \                  \
                  ||a *\2 + x *log (a) - 2*x*log(a)/         3        |
  /               ||--------------------------------  for log (a) != 0|
 |                ||               3                                  |
 |  2  x          ||            log (a)                               |
 | x *a  dx = C + |<                                                  |
 |                ||                3                                 |
/                 ||               x                                  |
                  ||               --                    otherwise    |
                  ||               3                                  |
                  \\                                                  /
∫axx2 dx=C+{ax(x2log⁡(a)2−2xlog⁡(a)+2)log⁡(a)3for log⁡(a)3≠0x33otherwise\int a^{x} x^{2}\, dx = C + \begin{cases} \frac{a^{x} \left(x^{2} \log{\left(a \right)}^{2} - 2 x \log{\left(a \right)} + 2\right)}{\log{\left(a \right)}^{3}} & \text{for}\: \log{\left(a \right)}^{3} \neq 0 \\\frac{x^{3}}{3} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/              /       2              \                                   
|     2      a*\2 + log (a) - 2*log(a)/                                   
|- ------- + --------------------------  for Or(And(a >= 0, a < 1), a > 1)
<     3                  3                                                
|  log (a)            log (a)                                             
|                                                                         
\                 1/3                                otherwise
{a(log⁡(a)2−2log⁡(a)+2)log⁡(a)3−2log⁡(a)3for (a≥0∧a<1)∨a>113otherwise\begin{cases} \frac{a \left(\log{\left(a \right)}^{2} - 2 \log{\left(a \right)} + 2\right)}{\log{\left(a \right)}^{3}} - \frac{2}{\log{\left(a \right)}^{3}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\\frac{1}{3} & \text{otherwise} \end{cases} 
=
= 
/              /       2              \                                   
|     2      a*\2 + log (a) - 2*log(a)/                                   
|- ------- + --------------------------  for Or(And(a >= 0, a < 1), a > 1)
<     3                  3                                                
|  log (a)            log (a)                                             
|                                                                         
\                 1/3                                otherwise
{a(log⁡(a)2−2log⁡(a)+2)log⁡(a)3−2log⁡(a)3for (a≥0∧a<1)∨a>113otherwise\begin{cases} \frac{a \left(\log{\left(a \right)}^{2} - 2 \log{\left(a \right)} + 2\right)}{\log{\left(a \right)}^{3}} - \frac{2}{\log{\left(a \right)}^{3}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\\frac{1}{3} & \text{otherwise} \end{cases} 
Piecewise((-2/log(a)^3 + a*(2 + log(a)^2 - 2*log(a))/log(a)^3, (a > 1)∨((a >= 0)∧(a < 1))), (1/3, True))

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

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