Sr Examen

Otras calculadoras

Resolución de integrales/ x^2-9/ x^2sqrt(x^2-9)

Integral de x^2sqrt(x^2-9) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |        ________   
 |   2   /  2        
 |  x *\/  x  - 9  dx
 |                   
/                    
0
∫01x2x2−9 dx\int\limits_{0}^{1} x^{2} \sqrt{x^{2} - 9}\, dx 
Integral(x^2*sqrt(x^2 - 9), (x, 0, 1))
Respuesta (Indefinida) [src] 
                           //          /x\                                                                 \
                           ||  81*acosh|-|           3               5                             | 2|    |
                           ||          \3/       27*x               x               81*x           |x |    |
  /                        ||- ----------- - -------------- + -------------- + --------------  for ---- > 1|
 |                         ||       8             _________        _________        _________       9      |
 |       ________          ||                    /       2        /       2        /       2               |
 |  2   /  2               ||                8*\/  -9 + x     4*\/  -9 + x     8*\/  -9 + x                |
 | x *\/  x  - 9  dx = C + |<                                                                              |
 |                         ||           /x\                                                                |
/                          ||  81*I*asin|-|                           5                3                   |
                           ||           \3/       81*I*x           I*x           27*I*x                    |
                           ||  ------------ - ------------- - ------------- + -------------     otherwise  |
                           ||       8              ________        ________        ________                |
                           ||                     /      2        /      2        /      2                 |
                           \\                 8*\/  9 - x     4*\/  9 - x     8*\/  9 - x                  /
∫x2x2−9 dx=C+{x54x2−9−27x38x2−9+81x8x2−9−81acosh⁡(x3)8for ∣x2∣9>1−ix549−x2+27ix389−x2−81ix89−x2+81iasin⁡(x3)8otherwise\int x^{2} \sqrt{x^{2} - 9}\, dx = C + \begin{cases} \frac{x^{5}}{4 \sqrt{x^{2} - 9}} - \frac{27 x^{3}}{8 \sqrt{x^{2} - 9}} + \frac{81 x}{8 \sqrt{x^{2} - 9}} - \frac{81 \operatorname{acosh}{\left(\frac{x}{3} \right)}}{8} & \text{for}\: \frac{\left|{x^{2}}\right|}{9} > 1 \\- \frac{i x^{5}}{4 \sqrt{9 - x^{2}}} + \frac{27 i x^{3}}{8 \sqrt{9 - x^{2}}} - \frac{81 i x}{8 \sqrt{9 - x^{2}}} + \frac{81 i \operatorname{asin}{\left(\frac{x}{3} \right)}}{8} & \text{otherwise} \end{cases}
Simplificar
Gráfica
0.000000.000050.000100.000150.000200.000250.000300.0003501
Trazar el gráfico f(x)
Respuesta [src] 
  1                                                                                                                                         
  /                                                                                                                                         
 |                                                                                                                                          
 |  /                                              2                2               6                 4                4            2       
 |  |         27                81             81*x             81*x               x               5*x             27*x            x        
 |  |- ---------------- + -------------- - -------------- - -------------- - -------------- + -------------- + --------------  for -- > 1   
 |  |         _________        _________              3/2        _________              3/2        _________              3/2      9        
 |  |        /       2        /       2      /      2\          /       2      /      2\          /       2      /      2\                  
 |  |       /       x     8*\/  -9 + x     8*\-9 + x /      8*\/  -9 + x     4*\-9 + x /      4*\/  -9 + x     8*\-9 + x /                  
 |  |  8*  /   -1 + --                                                                                                                      
 |  |    \/         9                                                                                                                       
 |  <                                                                                                                                     dx
 |  |                                                2               4              6                4               2                      
 |  |          81*I             27*I           81*I*x           5*I*x            I*x           27*I*x          81*I*x                       
 |  |   - ------------- + --------------- - ------------- - ------------- - ------------- + ------------- + -------------      otherwise    
 |  |          ________          ________             3/2        ________             3/2             3/2        ________                   
 |  |         /      2          /      2      /     2\          /      2      /     2\        /     2\          /      2                    
 |  |     8*\/  9 - x          /      x     8*\9 - x /      4*\/  9 - x     4*\9 - x /      8*\9 - x /      8*\/  9 - x                     
 |  |                     8*  /   1 - --                                                                                                    
 |  \                       \/        9                                                                                                     
 |                                                                                                                                          
/                                                                                                                                           
0
∫01{−x64(x2−9)32+5x44x2−9+27x48(x2−9)32−81x28x2−9−81x28(x2−9)32+818x2−9−278x29−1for x29>1−ix64(9−x2)32−5ix449−x2+27ix48(9−x2)32+81ix289−x2−81ix28(9−x2)32−81i89−x2+27i81−x29otherwise dx\int\limits_{0}^{1} \begin{cases} - \frac{x^{6}}{4 \left(x^{2} - 9\right)^{\frac{3}{2}}} + \frac{5 x^{4}}{4 \sqrt{x^{2} - 9}} + \frac{27 x^{4}}{8 \left(x^{2} - 9\right)^{\frac{3}{2}}} - \frac{81 x^{2}}{8 \sqrt{x^{2} - 9}} - \frac{81 x^{2}}{8 \left(x^{2} - 9\right)^{\frac{3}{2}}} + \frac{81}{8 \sqrt{x^{2} - 9}} - \frac{27}{8 \sqrt{\frac{x^{2}}{9} - 1}} & \text{for}\: \frac{x^{2}}{9} > 1 \\- \frac{i x^{6}}{4 \left(9 - x^{2}\right)^{\frac{3}{2}}} - \frac{5 i x^{4}}{4 \sqrt{9 - x^{2}}} + \frac{27 i x^{4}}{8 \left(9 - x^{2}\right)^{\frac{3}{2}}} + \frac{81 i x^{2}}{8 \sqrt{9 - x^{2}}} - \frac{81 i x^{2}}{8 \left(9 - x^{2}\right)^{\frac{3}{2}}} - \frac{81 i}{8 \sqrt{9 - x^{2}}} + \frac{27 i}{8 \sqrt{1 - \frac{x^{2}}{9}}} & \text{otherwise} \end{cases}\, dx 
=
= 
  1                                                                                                                                         
  /                                                                                                                                         
 |                                                                                                                                          
 |  /                                              2                2               6                 4                4            2       
 |  |         27                81             81*x             81*x               x               5*x             27*x            x        
 |  |- ---------------- + -------------- - -------------- - -------------- - -------------- + -------------- + --------------  for -- > 1   
 |  |         _________        _________              3/2        _________              3/2        _________              3/2      9        
 |  |        /       2        /       2      /      2\          /       2      /      2\          /       2      /      2\                  
 |  |       /       x     8*\/  -9 + x     8*\-9 + x /      8*\/  -9 + x     4*\-9 + x /      4*\/  -9 + x     8*\-9 + x /                  
 |  |  8*  /   -1 + --                                                                                                                      
 |  |    \/         9                                                                                                                       
 |  <                                                                                                                                     dx
 |  |                                                2               4              6                4               2                      
 |  |          81*I             27*I           81*I*x           5*I*x            I*x           27*I*x          81*I*x                       
 |  |   - ------------- + --------------- - ------------- - ------------- - ------------- + ------------- + -------------      otherwise    
 |  |          ________          ________             3/2        ________             3/2             3/2        ________                   
 |  |         /      2          /      2      /     2\          /      2      /     2\        /     2\          /      2                    
 |  |     8*\/  9 - x          /      x     8*\9 - x /      4*\/  9 - x     4*\9 - x /      8*\9 - x /      8*\/  9 - x                     
 |  |                     8*  /   1 - --                                                                                                    
 |  \                       \/        9                                                                                                     
 |                                                                                                                                          
/                                                                                                                                           
0
∫01{−x64(x2−9)32+5x44x2−9+27x48(x2−9)32−81x28x2−9−81x28(x2−9)32+818x2−9−278x29−1for x29>1−ix64(9−x2)32−5ix449−x2+27ix48(9−x2)32+81ix289−x2−81ix28(9−x2)32−81i89−x2+27i81−x29otherwise dx\int\limits_{0}^{1} \begin{cases} - \frac{x^{6}}{4 \left(x^{2} - 9\right)^{\frac{3}{2}}} + \frac{5 x^{4}}{4 \sqrt{x^{2} - 9}} + \frac{27 x^{4}}{8 \left(x^{2} - 9\right)^{\frac{3}{2}}} - \frac{81 x^{2}}{8 \sqrt{x^{2} - 9}} - \frac{81 x^{2}}{8 \left(x^{2} - 9\right)^{\frac{3}{2}}} + \frac{81}{8 \sqrt{x^{2} - 9}} - \frac{27}{8 \sqrt{\frac{x^{2}}{9} - 1}} & \text{for}\: \frac{x^{2}}{9} > 1 \\- \frac{i x^{6}}{4 \left(9 - x^{2}\right)^{\frac{3}{2}}} - \frac{5 i x^{4}}{4 \sqrt{9 - x^{2}}} + \frac{27 i x^{4}}{8 \left(9 - x^{2}\right)^{\frac{3}{2}}} + \frac{81 i x^{2}}{8 \sqrt{9 - x^{2}}} - \frac{81 i x^{2}}{8 \left(9 - x^{2}\right)^{\frac{3}{2}}} - \frac{81 i}{8 \sqrt{9 - x^{2}}} + \frac{27 i}{8 \sqrt{1 - \frac{x^{2}}{9}}} & \text{otherwise} \end{cases}\, dx 
Integral(Piecewise((-27/(8*sqrt(-1 + x^2/9)) + 81/(8*sqrt(-9 + x^2)) - 81*x^2/(8*(-9 + x^2)^(3/2)) - 81*x^2/(8*sqrt(-9 + x^2)) - x^6/(4*(-9 + x^2)^(3/2)) + 5*x^4/(4*sqrt(-9 + x^2)) + 27*x^4/(8*(-9 + x^2)^(3/2)), x^2/9 > 1), (-81*i/(8*sqrt(9 - x^2)) + 27*i/(8*sqrt(1 - x^2/9)) - 81*i*x^2/(8*(9 - x^2)^(3/2)) - 5*i*x^4/(4*sqrt(9 - x^2)) - i*x^6/(4*(9 - x^2)^(3/2)) + 27*i*x^4/(8*(9 - x^2)^(3/2)) + 81*i*x^2/(8*sqrt(9 - x^2)), True)), (x, 0, 1))
Respuesta numérica [src] 
(0.0 + 0.965974974070068j)
(0.0 + 0.965974974070068j)

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

    © Sr Examen – Калькулятор