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Resolución de integrales/ 1/((10x+5)*ln(10x+5))

Integral de 1/((10x+5)*ln(10x+5)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  a                            
  /                            
 |                             
 |             1               
 |  ------------------------ dx
 |  (10*x + 5)*log(10*x + 5)   
 |                             
/                              
1
∫1a1(10x+5)log⁡(10x+5) dx\int\limits_{1}^{a} \frac{1}{\left(10 x + 5\right) \log{\left(10 x + 5 \right)}}\, dx 
Integral(1/((10*x + 5)*log(10*x + 5)), (x, 1, a))
Respuesta (Indefinida) [src] 
  /                                                    
 |                                                     
 |            1                      log(log(5 + 10*x))
 | ------------------------ dx = C + ------------------
 | (10*x + 5)*log(10*x + 5)                  10        
 |                                                     
/
∫1(10x+5)log⁡(10x+5) dx=C+log⁡(log⁡(10x+5))10\int \frac{1}{\left(10 x + 5\right) \log{\left(10 x + 5 \right)}}\, dx = C + \frac{\log{\left(\log{\left(10 x + 5 \right)} \right)}}{10}
Simplificar
Respuesta [src] 
  log(log(15))   log(log(5 + 10*a))
- ------------ + ------------------
       10                10
log⁡(log⁡(10a+5))10−log⁡(log⁡(15))10\frac{\log{\left(\log{\left(10 a + 5 \right)} \right)}}{10} - \frac{\log{\left(\log{\left(15 \right)} \right)}}{10} 
=
= 
  log(log(15))   log(log(5 + 10*a))
- ------------ + ------------------
       10                10
log⁡(log⁡(10a+5))10−log⁡(log⁡(15))10\frac{\log{\left(\log{\left(10 a + 5 \right)} \right)}}{10} - \frac{\log{\left(\log{\left(15 \right)} \right)}}{10} 
-log(log(15))/10 + log(log(5 + 10*a))/10

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

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