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Resolución de integrales/ (x-6)/ sqrt(x)/ ((sqrt(x))*1)/(x-6)

Integral de ((sqrt(x))*1)/(x-6) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 49         
  /         
 |          
 |    ___   
 |  \/ x    
 |  ----- dx
 |  x - 6   
 |          
/           
25
∫2549xx−6 dx\int\limits_{25}^{49} \frac{\sqrt{x}}{x - 6}\, dx 
Integral(sqrt(x)/(x - 6), (x, 25, 49))
Respuesta (Indefinida) [src] 
                               //            /  ___   ___\            \
                               ||   ___      |\/ 6 *\/ x |            |
  /                            ||-\/ 6 *acoth|-----------|            |
 |                             ||            \     6     /            |
 |   ___                       ||--------------------------  for x > 6|
 | \/ x               ___      ||            6                        |
 | ----- dx = C + 2*\/ x  + 12*|<                                     |
 | x - 6                       ||            /  ___   ___\            |
 |                             ||   ___      |\/ 6 *\/ x |            |
/                              ||-\/ 6 *atanh|-----------|            |
                               ||            \     6     /            |
                               ||--------------------------  for x < 6|
                               \\            6                        /
∫xx−6 dx=C+2x+12({−6acoth⁡(6x6)6for x>6−6atanh⁡(6x6)6for x<6)\int \frac{\sqrt{x}}{x - 6}\, dx = C + 2 \sqrt{x} + 12 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \sqrt{x}}{6} \right)}}{6} & \text{for}\: x > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \sqrt{x}}{6} \right)}}{6} & \text{for}\: x < 6 \end{cases}\right)
Simplificar
Gráfica
25.027.530.032.535.037.540.042.545.047.5020
Trazar el gráfico f(x)
Respuesta [src] 
      ___    /      ___\     ___    /      ___\     ___    /      ___\     ___    /      ___\
4 + \/ 6 *log\5 + \/ 6 / + \/ 6 *log\7 - \/ 6 / - \/ 6 *log\5 - \/ 6 / - \/ 6 *log\7 + \/ 6 /
−6log⁡(6+7)−6log⁡(5−6)+6log⁡(7−6)+4+6log⁡(6+5)- \sqrt{6} \log{\left(\sqrt{6} + 7 \right)} - \sqrt{6} \log{\left(5 - \sqrt{6} \right)} + \sqrt{6} \log{\left(7 - \sqrt{6} \right)} + 4 + \sqrt{6} \log{\left(\sqrt{6} + 5 \right)} 
=
= 
      ___    /      ___\     ___    /      ___\     ___    /      ___\     ___    /      ___\
4 + \/ 6 *log\5 + \/ 6 / + \/ 6 *log\7 - \/ 6 / - \/ 6 *log\5 - \/ 6 / - \/ 6 *log\7 + \/ 6 /
−6log⁡(6+7)−6log⁡(5−6)+6log⁡(7−6)+4+6log⁡(6+5)- \sqrt{6} \log{\left(\sqrt{6} + 7 \right)} - \sqrt{6} \log{\left(5 - \sqrt{6} \right)} + \sqrt{6} \log{\left(7 - \sqrt{6} \right)} + 4 + \sqrt{6} \log{\left(\sqrt{6} + 5 \right)} 
4 + sqrt(6)*log(5 + sqrt(6)) + sqrt(6)*log(7 - sqrt(6)) - sqrt(6)*log(5 - sqrt(6)) - sqrt(6)*log(7 + sqrt(6))
Respuesta numérica [src] 
4.83559621346543
4.83559621346543

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

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