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Resolución de integrales/ (x-3)/ (x+1)/ (2x+3)/ (2x+3)e^-((x-3)(x+1))

Integral de (2x+3)e^-((x-3)(x+1)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                               
  /                               
 |                                
 |             -(x - 3)*(x + 1)   
 |  (2*x + 3)*E                 dx
 |                                
/                                 
-oo
∫−∞∞e−(x−3)(x+1)(2x+3) dx\int\limits_{-\infty}^{\infty} e^{- \left(x - 3\right) \left(x + 1\right)} \left(2 x + 3\right)\, dx 
Integral((2*x + 3)*E^(-(x - 3)*(x + 1)), (x, -oo, oo))
Respuesta (Indefinida) [src] 
                                        /    /                     /            \   
  /                                     |   |                     |             |   
 |                                      |   |      2              |    2        |   
 |            -(x - 3)*(x + 1)          |   |    -x   2*x         |  -x   2*x   |  3
 | (2*x + 3)*E                 dx = C + |2* | x*e   *e    dx + 3* | e   *e    dx|*e 
 |                                      |   |                     |             |   
/                                       \  /                     /              /
∫e−(x−3)(x+1)(2x+3) dx=C+(3∫e2xe−x2 dx+2∫xe2xe−x2 dx)e3\int e^{- \left(x - 3\right) \left(x + 1\right)} \left(2 x + 3\right)\, dx = C + \left(3 \int e^{2 x} e^{- x^{2}}\, dx + 2 \int x e^{2 x} e^{- x^{2}}\, dx\right) e^{3}
Simplificar
Respuesta [src] 
                                                                          ____                4       ____          4
/   -4       ____              \  4   /      ____            -4\  4   9*\/ pi *(2 - erfc(2))*e    9*\/ pi *erfc(2)*e 
\- e   - 2*\/ pi *(2 - erfc(2))/*e  + \- 2*\/ pi *erfc(2) + e  /*e  + ------------------------- + -------------------
                                                                                  2                        2
(−2π(2−erfc⁡(2))−e−4)e4+(−2πerfc⁡(2)+e−4)e4+9πe4erfc⁡(2)2+9π(2−erfc⁡(2))e42\left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) - e^{-4}\right) e^{4} + \left(- 2 \sqrt{\pi} \operatorname{erfc}{\left(2 \right)} + e^{-4}\right) e^{4} + \frac{9 \sqrt{\pi} e^{4} \operatorname{erfc}{\left(2 \right)}}{2} + \frac{9 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) e^{4}}{2} 
=
= 
                                                                          ____                4       ____          4
/   -4       ____              \  4   /      ____            -4\  4   9*\/ pi *(2 - erfc(2))*e    9*\/ pi *erfc(2)*e 
\- e   - 2*\/ pi *(2 - erfc(2))/*e  + \- 2*\/ pi *erfc(2) + e  /*e  + ------------------------- + -------------------
                                                                                  2                        2
(−2π(2−erfc⁡(2))−e−4)e4+(−2πerfc⁡(2)+e−4)e4+9πe4erfc⁡(2)2+9π(2−erfc⁡(2))e42\left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) - e^{-4}\right) e^{4} + \left(- 2 \sqrt{\pi} \operatorname{erfc}{\left(2 \right)} + e^{-4}\right) e^{4} + \frac{9 \sqrt{\pi} e^{4} \operatorname{erfc}{\left(2 \right)}}{2} + \frac{9 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(2 \right)}\right) e^{4}}{2} 
(-exp(-4) - 2*sqrt(pi)*(2 - erfc(2)))*exp(4) + (-2*sqrt(pi)*erfc(2) + exp(-4))*exp(4) + 9*sqrt(pi)*(2 - erfc(2))*exp(4)/2 + 9*sqrt(pi)*erfc(2)*exp(4)/2
Respuesta numérica [src] 
483.863506392818
483.863506392818

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

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