Sr Examen

Otras calculadoras

Resolución de integrales/ (ln(x)+2)/(x(ln^2(x)+2ln(x)+5))

Integral de (ln(x)+2)/(x(ln^2(x)+2ln(x)+5)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                              
  /                              
 |                               
 |          log(x) + 2           
 |  -------------------------- dx
 |    /   2                  \   
 |  x*\log (x) + 2*log(x) + 5/   
 |                               
/                                
0
∫01log⁡(x)+2x((log⁡(x)2+2log⁡(x))+5) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}\right) + 5\right)}\, dx 
Integral((log(x) + 2)/((x*(log(x)^2 + 2*log(x) + 5))), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                        /1   log(x)\                              
 |                                     atan|- + ------|      /       2              \
 |         log(x) + 2                      \2     2   /   log\5 + log (x) + 2*log(x)/
 | -------------------------- dx = C + ---------------- + ---------------------------
 |   /   2                  \                 2                        2             
 | x*\log (x) + 2*log(x) + 5/                                                        
 |                                                                                   
/
∫log⁡(x)+2x((log⁡(x)2+2log⁡(x))+5) dx=C+log⁡(log⁡(x)2+2log⁡(x)+5)2+atan⁡(log⁡(x)2+12)2\int \frac{\log{\left(x \right)} + 2}{x \left(\left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}\right) + 5\right)}\, dx = C + \frac{\log{\left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)} + 5 \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{\log{\left(x \right)}}{2} + \frac{1}{2} \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1000500
Trazar el gráfico f(x)
Respuesta [src] 
  1                              
  /                              
 |                               
 |          2 + log(x)           
 |  -------------------------- dx
 |    /       2              \   
 |  x*\5 + log (x) + 2*log(x)/   
 |                               
/                                
0
∫01log⁡(x)+2x(log⁡(x)2+2log⁡(x)+5) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)} + 5\right)}\, dx 
=
= 
  1                              
  /                              
 |                               
 |          2 + log(x)           
 |  -------------------------- dx
 |    /       2              \   
 |  x*\5 + log (x) + 2*log(x)/   
 |                               
/                                
0
∫01log⁡(x)+2x(log⁡(x)2+2log⁡(x)+5) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)} + 5\right)}\, dx 
Integral((2 + log(x))/(x*(5 + log(x)^2 + 2*log(x))), (x, 0, 1))
Respuesta numérica [src] 
-1.96563684159417
-1.96563684159417

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

    © Sr Examen – Калькулятор