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Resolución de integrales/ x^3+5/ 2*x/(x^3+5)

Integral de 2*x/(x^3+5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo          
  /          
 |           
 |   2*x     
 |  ------ dx
 |   3       
 |  x  + 5   
 |           
/            
2
∫2∞2xx3+5 dx\int\limits_{2}^{\infty} \frac{2 x}{x^{3} + 5}\, dx 
Integral((2*x)/(x^3 + 5), (x, 2, oo))
Respuesta (Indefinida) [src] 
                                                                                            /    ___         ___  2/3\
  /                                                                            ___  2/3     |  \/ 3    2*x*\/ 3 *5   |
 |                    2/3    /    3 ___\    2/3    / 2/3    2     3 ___\   2*\/ 3 *5   *atan|- ----- + --------------|
 |  2*x            2*5   *log\x + \/ 5 /   5   *log\5    + x  - x*\/ 5 /                    \    3           15      /
 | ------ dx = C - --------------------- + ----------------------------- + -------------------------------------------
 |  3                        15                          15                                     15                    
 | x  + 5                                                                                                             
 |                                                                                                                    
/
∫2xx3+5 dx=C−2⋅523log⁡(x+53)15+523log⁡(x2−53x+523)15+23⋅523atan⁡(23⋅523x15−33)15\int \frac{2 x}{x^{3} + 5}\, dx = C - \frac{2 \cdot 5^{\frac{2}{3}} \log{\left(x + \sqrt[3]{5} \right)}}{15} + \frac{5^{\frac{2}{3}} \log{\left(x^{2} - \sqrt[3]{5} x + 5^{\frac{2}{3}} \right)}}{15} + \frac{2 \sqrt{3} \cdot 5^{\frac{2}{3}} \operatorname{atan}{\left(\frac{2 \sqrt{3} \cdot 5^{\frac{2}{3}} x}{15} - \frac{\sqrt{3}}{3} \right)}}{15}
Simplificar
Gráfica
2.00002.01002.00102.00202.00302.00402.00502.00602.00702.00802.00900.10.4
Trazar el gráfico f(x)
Respuesta [src] 
/                                                /           pi*I\                   /           5*pi*I\\           
|                                      -pi*I     |           ----|           pi*I    |           ------||           
|          /    3 ___  pi*I\           ------    |    3 ___   3  |           ----    |    3 ___    3   ||           
|   2/3    |    \/ 5 *e    |      2/3    3       |    \/ 5 *e    |      2/3   3      |    \/ 5 *e      ||           
|2*5   *log|1 - -----------|   2*5   *e      *log|1 - -----------|   2*5   *e    *log|1 - -------------||           
|          \         2     /                     \         2     /                   \          2      /|           
|--------------------------- - ----------------------------------- - -----------------------------------|*Gamma(1/3)
\             15                                15                                    15                /           
--------------------------------------------------------------------------------------------------------------------
                                                    3*Gamma(4/3)
(−2⋅523eiπ3log⁡(−53e5iπ32+1)15+2⋅523log⁡(−53eiπ2+1)15−2⋅523e−iπ3log⁡(1−53eiπ32)15)Γ(13)3Γ(43)\frac{\left(- \frac{2 \cdot 5^{\frac{2}{3}} e^{\frac{i \pi}{3}} \log{\left(- \frac{\sqrt[3]{5} e^{\frac{5 i \pi}{3}}}{2} + 1 \right)}}{15} + \frac{2 \cdot 5^{\frac{2}{3}} \log{\left(- \frac{\sqrt[3]{5} e^{i \pi}}{2} + 1 \right)}}{15} - \frac{2 \cdot 5^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{5} e^{\frac{i \pi}{3}}}{2} \right)}}{15}\right) \Gamma\left(\frac{1}{3}\right)}{3 \Gamma\left(\frac{4}{3}\right)} 
=
= 
/                                                /           pi*I\                   /           5*pi*I\\           
|                                      -pi*I     |           ----|           pi*I    |           ------||           
|          /    3 ___  pi*I\           ------    |    3 ___   3  |           ----    |    3 ___    3   ||           
|   2/3    |    \/ 5 *e    |      2/3    3       |    \/ 5 *e    |      2/3   3      |    \/ 5 *e      ||           
|2*5   *log|1 - -----------|   2*5   *e      *log|1 - -----------|   2*5   *e    *log|1 - -------------||           
|          \         2     /                     \         2     /                   \          2      /|           
|--------------------------- - ----------------------------------- - -----------------------------------|*Gamma(1/3)
\             15                                15                                    15                /           
--------------------------------------------------------------------------------------------------------------------
                                                    3*Gamma(4/3)
(−2⋅523eiπ3log⁡(−53e5iπ32+1)15+2⋅523log⁡(−53eiπ2+1)15−2⋅523e−iπ3log⁡(1−53eiπ32)15)Γ(13)3Γ(43)\frac{\left(- \frac{2 \cdot 5^{\frac{2}{3}} e^{\frac{i \pi}{3}} \log{\left(- \frac{\sqrt[3]{5} e^{\frac{5 i \pi}{3}}}{2} + 1 \right)}}{15} + \frac{2 \cdot 5^{\frac{2}{3}} \log{\left(- \frac{\sqrt[3]{5} e^{i \pi}}{2} + 1 \right)}}{15} - \frac{2 \cdot 5^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{5} e^{\frac{i \pi}{3}}}{2} \right)}}{15}\right) \Gamma\left(\frac{1}{3}\right)}{3 \Gamma\left(\frac{4}{3}\right)} 
(2*5^(2/3)*log(1 - 5^(1/3)*exp_polar(pi*i)/2)/15 - 2*5^(2/3)*exp(-pi*i/3)*log(1 - 5^(1/3)*exp_polar(pi*i/3)/2)/15 - 2*5^(2/3)*exp(pi*i/3)*log(1 - 5^(1/3)*exp_polar(5*pi*i/3)/2)/15)*gamma(1/3)/(3*gamma(4/3))

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

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