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Resolución de integrales/ (x+1)/ exp((x/2))*(x+1)^(1/2)

Integral de exp((x/2))*(x+1)^(1/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  6                
  /                
 |                 
 |   x             
 |   -             
 |   2   _______   
 |  e *\/ x + 1  dx
 |                 
/                  
1
∫16x+1ex2 dx\int\limits_{1}^{6} \sqrt{x + 1} e^{\frac{x}{2}}\, dx 
Integral(exp(x/2)*sqrt(x + 1), (x, 1, 6))
Respuesta (Indefinida) [src] 
                                           /           /  ___   ________\                     1   x\      
  /                                        |  ____     |\/ 2 *\/ -1 - x |                     - + -|      
 |                                         |\/ pi *erfc|----------------|     ___   ________  2   2|      
 |  x                        ___   _______ |           \       2        /   \/ 2 *\/ -1 - x *e     |  -1/2
 |  -                    2*\/ 2 *\/ 1 + x *|----------------------------- + -----------------------|*e    
 |  2   _______                            \              2                            2           /      
 | e *\/ x + 1  dx = C + ---------------------------------------------------------------------------------
 |                                                             ________                                   
/                                                            \/ -1 - x
∫x+1ex2 dx=C+22x+1(2−x−1ex2+122+πerfc⁡(2−x−12)2)−x−1e12\int \sqrt{x + 1} e^{\frac{x}{2}}\, dx = C + \frac{2 \sqrt{2} \sqrt{x + 1} \left(\frac{\sqrt{2} \sqrt{- x - 1} e^{\frac{x}{2} + \frac{1}{2}}}{2} + \frac{\sqrt{\pi} \operatorname{erfc}{\left(\frac{\sqrt{2} \sqrt{- x - 1}}{2} \right)}}{2}\right)}{\sqrt{- x - 1} e^{\frac{1}{2}}}
Simplificar
Gráfica
1.06.01.52.02.53.03.54.04.55.05.50100
Trazar el gráfico f(x)
Respuesta [src] 
                                                                         /                                                                   /  ____\\      
                                                                         |                                                    ___   ____     |\/ 14 ||      
                                                                         |               /      /  ____\     ____  7/2\   7*\/ 2 *\/ pi *erfi|------||      
    /  ___   ____             ___   ____ /3*erfi(1)     E   \\  -1/2     |    ___   ____ |      |\/ 14 |   \/ 14 *e   |                      \  2   /|  -1/2
- 2*|\/ 2 *\/ pi *erfi(1) - \/ 2 *\/ pi *|--------- - ------||*e     + 2*|- \/ 2 *\/ pi *|4*erfi|------| - -----------| + ---------------------------|*e    
    |                                    |    2         ____||           |               |      \  2   /         ____ |                2             |      
    \                                    \            \/ pi //           \               \                   2*\/ pi  /                              /
−2(−2π(−eπ+3erfi⁡(1)2)+2πerfi⁡(1))e12+2(−2π(−14e722π+4erfi⁡(142))+72πerfi⁡(142)2)e12- \frac{2 \left(- \sqrt{2} \sqrt{\pi} \left(- \frac{e}{\sqrt{\pi}} + \frac{3 \operatorname{erfi}{\left(1 \right)}}{2}\right) + \sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(1 \right)}\right)}{e^{\frac{1}{2}}} + \frac{2 \left(- \sqrt{2} \sqrt{\pi} \left(- \frac{\sqrt{14} e^{\frac{7}{2}}}{2 \sqrt{\pi}} + 4 \operatorname{erfi}{\left(\frac{\sqrt{14}}{2} \right)}\right) + \frac{7 \sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\frac{\sqrt{14}}{2} \right)}}{2}\right)}{e^{\frac{1}{2}}} 
=
= 
                                                                         /                                                                   /  ____\\      
                                                                         |                                                    ___   ____     |\/ 14 ||      
                                                                         |               /      /  ____\     ____  7/2\   7*\/ 2 *\/ pi *erfi|------||      
    /  ___   ____             ___   ____ /3*erfi(1)     E   \\  -1/2     |    ___   ____ |      |\/ 14 |   \/ 14 *e   |                      \  2   /|  -1/2
- 2*|\/ 2 *\/ pi *erfi(1) - \/ 2 *\/ pi *|--------- - ------||*e     + 2*|- \/ 2 *\/ pi *|4*erfi|------| - -----------| + ---------------------------|*e    
    |                                    |    2         ____||           |               |      \  2   /         ____ |                2             |      
    \                                    \            \/ pi //           \               \                   2*\/ pi  /                              /
−2(−2π(−eπ+3erfi⁡(1)2)+2πerfi⁡(1))e12+2(−2π(−14e722π+4erfi⁡(142))+72πerfi⁡(142)2)e12- \frac{2 \left(- \sqrt{2} \sqrt{\pi} \left(- \frac{e}{\sqrt{\pi}} + \frac{3 \operatorname{erfi}{\left(1 \right)}}{2}\right) + \sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(1 \right)}\right)}{e^{\frac{1}{2}}} + \frac{2 \left(- \sqrt{2} \sqrt{\pi} \left(- \frac{\sqrt{14} e^{\frac{7}{2}}}{2 \sqrt{\pi}} + 4 \operatorname{erfi}{\left(\frac{\sqrt{14}}{2} \right)}\right) + \frac{7 \sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\frac{\sqrt{14}}{2} \right)}}{2}\right)}{e^{\frac{1}{2}}} 
-2*(sqrt(2)*sqrt(pi)*erfi(1) - sqrt(2)*sqrt(pi)*(3*erfi(1)/2 - E/sqrt(pi)))*exp(-1/2) + 2*(-sqrt(2)*sqrt(pi)*(4*erfi(sqrt(14)/2) - sqrt(14)*exp(7/2)/(2*sqrt(pi))) + 7*sqrt(2)*sqrt(pi)*erfi(sqrt(14)/2)/2)*exp(-1/2)
Respuesta numérica [src] 
85.398341378979
85.398341378979

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

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