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Resolución de integrales/ 5^(2*x)/ 5^x/(4+5^(2*x))

Integral de 5^x/(4+5^(2*x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |      x      
 |     5       
 |  -------- dx
 |       2*x   
 |  4 + 5      
 |             
/              
0
∫015x52x+4 dx\int\limits_{0}^{1} \frac{5^{x}}{5^{2 x} + 4}\, dx 
Integral(5^x/(4 + 5^(2*x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                      / x\
 |                       |5 |
 |     x             atan|--|
 |    5                  \2 /
 | -------- dx = C + --------
 |      2*x          2*log(5)
 | 4 + 5                     
 |                           
/
∫5x52x+4 dx=C+atan⁡(5x2)2log⁡(5)\int \frac{5^{x}}{5^{2 x} + 4}\, dx = C + \frac{\operatorname{atan}{\left(\frac{5^{x}}{2} \right)}}{2 \log{\left(5 \right)}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Trazar el gráfico f(x)
Respuesta [src] 
       /    2                           \          /    2                         \
RootSum\16*z  + 1, i -> i*log(625 + 8*i)/   RootSum\16*z  + 1, i -> i*log(1 + 8*i)/
----------------------------------------- - ---------------------------------------
                  log(5)                                     log(5)
−RootSum⁡(16z2+1,(i↦ilog⁡(8i+1)))log⁡(5)+RootSum⁡(16z2+1,(i↦ilog⁡(8i+625)))log⁡(5)- \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 1 \right)} \right)\right)}}{\log{\left(5 \right)}} + \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 625 \right)} \right)\right)}}{\log{\left(5 \right)}} 
=
= 
       /    2                           \          /    2                         \
RootSum\16*z  + 1, i -> i*log(625 + 8*i)/   RootSum\16*z  + 1, i -> i*log(1 + 8*i)/
----------------------------------------- - ---------------------------------------
                  log(5)                                     log(5)
−RootSum⁡(16z2+1,(i↦ilog⁡(8i+1)))log⁡(5)+RootSum⁡(16z2+1,(i↦ilog⁡(8i+625)))log⁡(5)- \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 1 \right)} \right)\right)}}{\log{\left(5 \right)}} + \frac{\operatorname{RootSum} {\left(16 z^{2} + 1, \left( i \mapsto i \log{\left(8 i + 625 \right)} \right)\right)}}{\log{\left(5 \right)}} 
RootSum(16*_z^2 + 1, Lambda(_i, _i*log(625 + 8*_i)))/log(5) - RootSum(16*_z^2 + 1, Lambda(_i, _i*log(1 + 8*_i)))/log(5)
Respuesta numérica [src] 
0.225744135597862
0.225744135597862

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

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