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Resolución de integrales/ sqrt^3/ sqrt(X)/ 1/(sqrt(X)*(sqrt^3(x)+36))

Integral de 1/(sqrt(X)*(sqrt^3(x)+36)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  9                       
  /                       
 |                        
 |           1            
 |  ------------------- dx
 |        /     3     \   
 |    ___ |  ___      |   
 |  \/ x *\\/ x   + 36/   
 |                        
/                         
4
∫491x((x)3+36) dx\int\limits_{4}^{9} \frac{1}{\sqrt{x} \left(\left(\sqrt{x}\right)^{3} + 36\right)}\, dx 
Integral(1/(sqrt(x)*((sqrt(x))^3 + 36)), (x, 4, 9))
Respuesta (Indefinida) [src] 
                                                                                                                  /    ___   3 ___  5/6   ___\
  /                                                                                                 2/3 6 ___     |  \/ 3    \/ 2 *3   *\/ x |
 |                               2/3    /         3 ___      2/3   ___\    2/3    / 2/3     ___\   2   *\/ 3 *atan|- ----- + ----------------|
 |          1                   6   *log\4*x + 24*\/ 6  - 4*6   *\/ x /   6   *log\6    + \/ x /                  \    3            9        /
 | ------------------- dx = C - --------------------------------------- + ---------------------- + -------------------------------------------
 |       /     3     \                            108                               54                                  18                    
 |   ___ |  ___      |                                                                                                                        
 | \/ x *\\/ x   + 36/                                                                                                                        
 |                                                                                                                                            
/
∫1x((x)3+36) dx=C+623log⁡(x+623)54−623log⁡(−4⋅623x+4x+2463)108+22336atan⁡(23⋅356x9−33)18\int \frac{1}{\sqrt{x} \left(\left(\sqrt{x}\right)^{3} + 36\right)}\, dx = C + \frac{6^{\frac{2}{3}} \log{\left(\sqrt{x} + 6^{\frac{2}{3}} \right)}}{54} - \frac{6^{\frac{2}{3}} \log{\left(- 4 \cdot 6^{\frac{2}{3}} \sqrt{x} + 4 x + 24 \sqrt[3]{6} \right)}}{108} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt[3]{2} \cdot 3^{\frac{5}{6}} \sqrt{x}}{9} - \frac{\sqrt{3}}{3} \right)}}{18}
Simplificar
Gráfica
4.09.04.55.05.56.06.57.07.58.08.50.000.05
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                                                                  /  ___   3 ___  5/6\                  /  ___     3 ___  5/6\
                                                                                                                    2/3 6 ___     |\/ 3    \/ 2 *3   |    2/3 6 ___     |\/ 3    2*\/ 2 *3   |
   2/3    /     2/3\    2/3    /         2/3      3 ___\    2/3    /     2/3\    2/3    /        2/3      3 ___\   2   *\/ 3 *atan|----- - ----------|   2   *\/ 3 *atan|----- - ------------|
  6   *log\2 + 6   /   6   *log\36 - 12*6    + 24*\/ 6 /   6   *log\3 + 6   /   6   *log\16 - 8*6    + 24*\/ 6 /                  \  3         3     /                  \  3          9      /
- ------------------ - --------------------------------- + ------------------ + -------------------------------- - ----------------------------------- + -------------------------------------
          54                          108                          54                         108                                   18                                     18
−623log⁡(−12⋅623+36+2463)108−623log⁡(2+623)54+22336atan⁡(−223⋅3569+33)18−22336atan⁡(−23⋅3563+33)18+623log⁡(−8⋅623+16+2463)108+623log⁡(3+623)54- \frac{6^{\frac{2}{3}} \log{\left(- 12 \cdot 6^{\frac{2}{3}} + 36 + 24 \sqrt[3]{6} \right)}}{108} - \frac{6^{\frac{2}{3}} \log{\left(2 + 6^{\frac{2}{3}} \right)}}{54} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{2 \sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{18} - \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{3} + \frac{\sqrt{3}}{3} \right)}}{18} + \frac{6^{\frac{2}{3}} \log{\left(- 8 \cdot 6^{\frac{2}{3}} + 16 + 24 \sqrt[3]{6} \right)}}{108} + \frac{6^{\frac{2}{3}} \log{\left(3 + 6^{\frac{2}{3}} \right)}}{54} 
=
= 
                                                                                                                                  /  ___   3 ___  5/6\                  /  ___     3 ___  5/6\
                                                                                                                    2/3 6 ___     |\/ 3    \/ 2 *3   |    2/3 6 ___     |\/ 3    2*\/ 2 *3   |
   2/3    /     2/3\    2/3    /         2/3      3 ___\    2/3    /     2/3\    2/3    /        2/3      3 ___\   2   *\/ 3 *atan|----- - ----------|   2   *\/ 3 *atan|----- - ------------|
  6   *log\2 + 6   /   6   *log\36 - 12*6    + 24*\/ 6 /   6   *log\3 + 6   /   6   *log\16 - 8*6    + 24*\/ 6 /                  \  3         3     /                  \  3          9      /
- ------------------ - --------------------------------- + ------------------ + -------------------------------- - ----------------------------------- + -------------------------------------
          54                          108                          54                         108                                   18                                     18
−623log⁡(−12⋅623+36+2463)108−623log⁡(2+623)54+22336atan⁡(−223⋅3569+33)18−22336atan⁡(−23⋅3563+33)18+623log⁡(−8⋅623+16+2463)108+623log⁡(3+623)54- \frac{6^{\frac{2}{3}} \log{\left(- 12 \cdot 6^{\frac{2}{3}} + 36 + 24 \sqrt[3]{6} \right)}}{108} - \frac{6^{\frac{2}{3}} \log{\left(2 + 6^{\frac{2}{3}} \right)}}{54} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{2 \sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{18} - \frac{2^{\frac{2}{3}} \sqrt[6]{3} \operatorname{atan}{\left(- \frac{\sqrt[3]{2} \cdot 3^{\frac{5}{6}}}{3} + \frac{\sqrt{3}}{3} \right)}}{18} + \frac{6^{\frac{2}{3}} \log{\left(- 8 \cdot 6^{\frac{2}{3}} + 16 + 24 \sqrt[3]{6} \right)}}{108} + \frac{6^{\frac{2}{3}} \log{\left(3 + 6^{\frac{2}{3}} \right)}}{54} 
-6^(2/3)*log(2 + 6^(2/3))/54 - 6^(2/3)*log(36 - 12*6^(2/3) + 24*6^(1/3))/108 + 6^(2/3)*log(3 + 6^(2/3))/54 + 6^(2/3)*log(16 - 8*6^(2/3) + 24*6^(1/3))/108 - 2^(2/3)*3^(1/6)*atan(sqrt(3)/3 - 2^(1/3)*3^(5/6)/3)/18 + 2^(2/3)*3^(1/6)*atan(sqrt(3)/3 - 2*2^(1/3)*3^(5/6)/9)/18
Respuesta numérica [src] 
0.0386954911044156
0.0386954911044156

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

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