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Resolución de integrales/ (1/3)/ (x-2)/ sqrt(x)/ sqrt(x)/(x-2)/(1/3)dx

Integral de sqrt(x)/(x-2)/(1/3)dx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |  /  ___\   
 |  |\/ x |   
 |  |-----|   
 |  \x - 2/   
 |  ------- dx
 |    1/3     
 |            
/             
0
1 / | | / ___\ | |\/ x | | |-----| | \x - 2/ | ------- dx | 1/3 | / 0 
Integral((sqrt(x)/(x - 2))/(1/3), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                              //            /  ___   ___\            \
 |                               ||   ___      |\/ 2 *\/ x |            |
 | /  ___\                       ||-\/ 2 *acoth|-----------|            |
 | |\/ x |                       ||            \     2     /            |
 | |-----|                       ||--------------------------  for x > 2|
 | \x - 2/              ___      ||            2                        |
 | ------- dx = C + 6*\/ x  + 12*|<                                     |
 |   1/3                         ||            /  ___   ___\            |
 |                               ||   ___      |\/ 2 *\/ x |            |
/                                ||-\/ 2 *atanh|-----------|            |
                                 ||            \     2     /            |
                                 ||--------------------------  for x < 2|
                                 \\            2                        /
/ // / ___ ___\ \ | || ___ |\/ 2 *\/ x | | | / ___\ ||-\/ 2 *acoth|-----------| | | |\/ x | || \ 2 / | | |-----| ||-------------------------- for x > 2| | \x - 2/ ___ || 2 | | ------- dx = C + 6*\/ x + 12*|< | | 1/3 || / ___ ___\ | | || ___ |\/ 2 *\/ x | | / ||-\/ 2 *atanh|-----------| | || \ 2 / | ||-------------------------- for x < 2| \\ 2 /
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.905-5
Trazar el gráfico f(x)
Respuesta [src] 
        ___ /          /  ___\\       ___    /      ___\       ___ /          /       ___\\       ___    /  ___\
6 - 3*\/ 2 *\pi*I + log\\/ 2 // - 3*\/ 2 *log\1 + \/ 2 / + 3*\/ 2 *\pi*I + log\-1 + \/ 2 // + 3*\/ 2 *log\\/ 2 /
−32log⁡(1+2)+32log⁡(2)+6−32(log⁡(2)+iπ)+32(log⁡(−1+2)+iπ)- 3 \sqrt{2} \log{\left(1 + \sqrt{2} \right)} + 3 \sqrt{2} \log{\left(\sqrt{2} \right)} + 6 - 3 \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right) + 3 \sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right) 
=
= 
        ___ /          /  ___\\       ___    /      ___\       ___ /          /       ___\\       ___    /  ___\
6 - 3*\/ 2 *\pi*I + log\\/ 2 // - 3*\/ 2 *log\1 + \/ 2 / + 3*\/ 2 *\pi*I + log\-1 + \/ 2 // + 3*\/ 2 *log\\/ 2 /
−32log⁡(1+2)+32log⁡(2)+6−32(log⁡(2)+iπ)+32(log⁡(−1+2)+iπ)- 3 \sqrt{2} \log{\left(1 + \sqrt{2} \right)} + 3 \sqrt{2} \log{\left(\sqrt{2} \right)} + 6 - 3 \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right) + 3 \sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right) 
6 - 3*sqrt(2)*(pi*i + log(sqrt(2))) - 3*sqrt(2)*log(1 + sqrt(2)) + 3*sqrt(2)*(pi*i + log(-1 + sqrt(2))) + 3*sqrt(2)*log(sqrt(2))
Respuesta numérica [src] 
-1.47870288168277
-1.47870288168277

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

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