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Resolución de integrales/ (2x+3)/ (1/((2x+3)ln(x+9)^2))

Integral de (1/((2x+3)ln(x+9)^2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                         
  /                         
 |                          
 |            1             
 |  --------------------- dx
 |               2          
 |  (2*x + 3)*log (x + 9)   
 |                          
/                           
1
∫1∞1(2x+3)log⁡(x+9)2 dx\int\limits_{1}^{\infty} \frac{1}{\left(2 x + 3\right) \log{\left(x + 9 \right)}^{2}}\, dx 
Integral(1/((2*x + 3)*log(x + 9)^2), (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                                    /                                                                          
 |                                    |                                                                           
 |           1                        |                        1                                     -9 - x       
 | --------------------- dx = C - 15* | ------------------------------------------------ dx + --------------------
 |              2                     |                   2                                   (3 + 2*x)*log(9 + x)
 | (2*x + 3)*log (x + 9)              | 9*log(9 + x) + 4*x *log(9 + x) + 12*x*log(9 + x)                          
 |                                    |                                                                           
/                                    /
∫1(2x+3)log⁡(x+9)2 dx=C+−x−9(2x+3)log⁡(x+9)−15∫14x2log⁡(x+9)+12xlog⁡(x+9)+9log⁡(x+9) dx\int \frac{1}{\left(2 x + 3\right) \log{\left(x + 9 \right)}^{2}}\, dx = C + \frac{- x - 9}{\left(2 x + 3\right) \log{\left(x + 9 \right)}} - 15 \int \frac{1}{4 x^{2} \log{\left(x + 9 \right)} + 12 x \log{\left(x + 9 \right)} + 9 \log{\left(x + 9 \right)}}\, dx
Simplificar
Respuesta [src] 
      oo                                                              
       /                                                              
      |                                                               
      |                         1                                 2   
- 15* |  ------------------------------------------------ dx + -------
      |                    2                                   log(10)
      |  9*log(9 + x) + 4*x *log(9 + x) + 12*x*log(9 + x)             
      |                                                               
     /                                                                
     1
−15∫1∞14x2log⁡(x+9)+12xlog⁡(x+9)+9log⁡(x+9) dx+2log⁡(10)- 15 \int\limits_{1}^{\infty} \frac{1}{4 x^{2} \log{\left(x + 9 \right)} + 12 x \log{\left(x + 9 \right)} + 9 \log{\left(x + 9 \right)}}\, dx + \frac{2}{\log{\left(10 \right)}} 
=
= 
      oo                                                              
       /                                                              
      |                                                               
      |                         1                                 2   
- 15* |  ------------------------------------------------ dx + -------
      |                    2                                   log(10)
      |  9*log(9 + x) + 4*x *log(9 + x) + 12*x*log(9 + x)             
      |                                                               
     /                                                                
     1
−15∫1∞14x2log⁡(x+9)+12xlog⁡(x+9)+9log⁡(x+9) dx+2log⁡(10)- 15 \int\limits_{1}^{\infty} \frac{1}{4 x^{2} \log{\left(x + 9 \right)} + 12 x \log{\left(x + 9 \right)} + 9 \log{\left(x + 9 \right)}}\, dx + \frac{2}{\log{\left(10 \right)}} 
-15*Integral(1/(9*log(9 + x) + 4*x^2*log(9 + x) + 12*x*log(9 + x)), (x, 1, oo)) + 2/log(10)

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

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