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Resolución de integrales/ 3^(2x)/ (3^x)/((3^(2x))+5)

Integral de (3^x)/((3^(2x))+5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |      x      
 |     3       
 |  -------- dx
 |   2*x       
 |  3    + 5   
 |             
/              
0
∫013x32x+5 dx\int\limits_{0}^{1} \frac{3^{x}}{3^{2 x} + 5}\, dx 
Integral(3^x/(3^(2*x) + 5), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                            / x   ___\
 |                     ___     |3 *\/ 5 |
 |     x             \/ 5 *atan|--------|
 |    3                        \   5    /
 | -------- dx = C + --------------------
 |  2*x                    5*log(3)      
 | 3    + 5                              
 |                                       
/
∫3x32x+5 dx=C+5atan⁡(3x55)5log⁡(3)\int \frac{3^{x}}{3^{2 x} + 5}\, dx = C + \frac{\sqrt{5} \operatorname{atan}{\left(\frac{3^{x} \sqrt{5}}{5} \right)}}{5 \log{\left(3 \right)}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901.0-1.0
Trazar el gráfico f(x)
Respuesta [src] 
       /    2                           \          /    2                          \
RootSum\20*z  + 1, i -> i*log(81 + 10*i)/   RootSum\20*z  + 1, i -> i*log(1 + 10*i)/
----------------------------------------- - ----------------------------------------
                  log(3)                                     log(3)
−RootSum⁡(20z2+1,(i↦ilog⁡(10i+1)))log⁡(3)+RootSum⁡(20z2+1,(i↦ilog⁡(10i+81)))log⁡(3)- \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 1 \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 81 \right)} \right)\right)}}{\log{\left(3 \right)}} 
=
= 
       /    2                           \          /    2                          \
RootSum\20*z  + 1, i -> i*log(81 + 10*i)/   RootSum\20*z  + 1, i -> i*log(1 + 10*i)/
----------------------------------------- - ----------------------------------------
                  log(3)                                     log(3)
−RootSum⁡(20z2+1,(i↦ilog⁡(10i+1)))log⁡(3)+RootSum⁡(20z2+1,(i↦ilog⁡(10i+81)))log⁡(3)- \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 1 \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(20 z^{2} + 1, \left( i \mapsto i \log{\left(10 i + 81 \right)} \right)\right)}}{\log{\left(3 \right)}} 
RootSum(20*_z^2 + 1, Lambda(_i, _i*log(81 + 10*_i)))/log(3) - RootSum(20*_z^2 + 1, Lambda(_i, _i*log(1 + 10*_i)))/log(3)
Respuesta numérica [src] 
0.2075004229341
0.2075004229341

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

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