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Resolución de integrales/ x^2-9/ rootx/ (dx)/(X^(2)rootx^2-9)

Integral de (dx)/(X^(2)rootx^2-9) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  6                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |          2       
 |   2   ___        
 |  x *\/ x   - 9   
 |                  
/                   
37                  
--                  
10
∫371061x2(x)2−9 dx\int\limits_{\frac{37}{10}}^{6} \frac{1}{x^{2} \left(\sqrt{x}\right)^{2} - 9}\, dx 
Integral(1/(x^2*(sqrt(x))^2 - 9), (x, 37/10, 6))
Respuesta (Indefinida) [src] 
                                    /  ___        5/6\                                                            
  /                       6 ___     |\/ 3    2*x*3   |                                             /     2       \
 |                        \/ 3 *atan|----- + --------|    2/3    / 2     3 ___      2/3\    2/3    |  ___     2/3|
 |       1                          \  3        9    /   3   *log\x  + 3*\/ 3  + x*3   /   3   *log\\/ x   - 3   /
 | ------------- dx = C - ---------------------------- - ------------------------------- + -----------------------
 |         2                           9                                54                            27          
 |  2   ___                                                                                                       
 | x *\/ x   - 9                                                                                                  
 |                                                                                                                
/
∫1x2(x)2−9 dx=C+323log⁡((x)2−323)27−323log⁡(x2+323x+333)54−36atan⁡(2⋅356x9+33)9\int \frac{1}{x^{2} \left(\sqrt{x}\right)^{2} - 9}\, dx = C + \frac{3^{\frac{2}{3}} \log{\left(\left(\sqrt{x}\right)^{2} - 3^{\frac{2}{3}} \right)}}{27} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + 3^{\frac{2}{3}} x + 3 \sqrt[3]{3} \right)}}{54} - \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}} x}{9} + \frac{\sqrt{3}}{3} \right)}}{9}
Simplificar
Gráfica
6.03.84.04.24.44.64.85.05.25.45.65.8-0.500.25
Trazar el gráfico f(x)
Respuesta [src] 
            /  ___      5/6\                                                                     /  ___       5/6\                                /                     2/3\
  6 ___     |\/ 3    4*3   |    2/3    /37    2/3\                                     6 ___     |\/ 3    37*3   |                         2/3    |1369     3 ___   37*3   |
  \/ 3 *atan|----- + ------|   3   *log|-- - 3   |    2/3    /       3 ___      2/3\   \/ 3 *atan|----- + -------|    2/3    /     2/3\   3   *log|---- + 3*\/ 3  + -------|
            \  3       3   /           \10       /   3   *log\36 + 3*\/ 3  + 6*3   /             \  3        45  /   3   *log\6 - 3   /           \100                 10  /
- -------------------------- - ------------------- - ------------------------------- + --------------------------- + ------------------ + ----------------------------------
              9                         27                          54                              9                        27                           54
−36atan⁡(33+4⋅3563)9−323log⁡(333+6⋅323+36)54−323log⁡(3710−323)27+323log⁡(6−323)27+323log⁡(333+37⋅32310+1369100)54+36atan⁡(33+37⋅35645)9- \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{4 \cdot 3^{\frac{5}{6}}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + 6 \cdot 3^{\frac{2}{3}} + 36 \right)}}{54} - \frac{3^{\frac{2}{3}} \log{\left(\frac{37}{10} - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(6 - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + \frac{37 \cdot 3^{\frac{2}{3}}}{10} + \frac{1369}{100} \right)}}{54} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{37 \cdot 3^{\frac{5}{6}}}{45} \right)}}{9} 
=
= 
            /  ___      5/6\                                                                     /  ___       5/6\                                /                     2/3\
  6 ___     |\/ 3    4*3   |    2/3    /37    2/3\                                     6 ___     |\/ 3    37*3   |                         2/3    |1369     3 ___   37*3   |
  \/ 3 *atan|----- + ------|   3   *log|-- - 3   |    2/3    /       3 ___      2/3\   \/ 3 *atan|----- + -------|    2/3    /     2/3\   3   *log|---- + 3*\/ 3  + -------|
            \  3       3   /           \10       /   3   *log\36 + 3*\/ 3  + 6*3   /             \  3        45  /   3   *log\6 - 3   /           \100                 10  /
- -------------------------- - ------------------- - ------------------------------- + --------------------------- + ------------------ + ----------------------------------
              9                         27                          54                              9                        27                           54
−36atan⁡(33+4⋅3563)9−323log⁡(333+6⋅323+36)54−323log⁡(3710−323)27+323log⁡(6−323)27+323log⁡(333+37⋅32310+1369100)54+36atan⁡(33+37⋅35645)9- \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{4 \cdot 3^{\frac{5}{6}}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + 6 \cdot 3^{\frac{2}{3}} + 36 \right)}}{54} - \frac{3^{\frac{2}{3}} \log{\left(\frac{37}{10} - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(6 - 3^{\frac{2}{3}} \right)}}{27} + \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} + \frac{37 \cdot 3^{\frac{2}{3}}}{10} + \frac{1369}{100} \right)}}{54} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{37 \cdot 3^{\frac{5}{6}}}{45} \right)}}{9} 
-3^(1/6)*atan(sqrt(3)/3 + 4*3^(5/6)/3)/9 - 3^(2/3)*log(37/10 - 3^(2/3))/27 - 3^(2/3)*log(36 + 3*3^(1/3) + 6*3^(2/3))/54 + 3^(1/6)*atan(sqrt(3)/3 + 37*3^(5/6)/45)/9 + 3^(2/3)*log(6 - 3^(2/3))/27 + 3^(2/3)*log(1369/100 + 3*3^(1/3) + 37*3^(2/3)/10)/54
Respuesta numérica [src] 
0.0253237823088052
0.0253237823088052

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

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