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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1/2           
   /            
  |             
  |      x      
  |     3       
  |  -------- dx
  |       2*x   
  |  1 + 3      
  |             
 /              
-1/2
∫−12123x32x+1 dx\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{3^{x}}{3^{2 x} + 1}\, dx 
Integral(3^x/(1 + 3^(2*x)), (x, -1/2, 1/2))
Respuesta (Indefinida) [src] 
  /                          
 |                           
 |     x                 / x\
 |    3              atan\3 /
 | -------- dx = C + --------
 |      2*x           log(3) 
 | 1 + 3                     
 |                           
/
∫3x32x+1 dx=C+atan⁡(3x)log⁡(3)\int \frac{3^{x}}{3^{2 x} + 1}\, dx = C + \frac{\operatorname{atan}{\left(3^{x} \right)}}{\log{\left(3 \right)}}
Simplificar
Gráfica
-0.50-0.40-0.30-0.20-0.100.500.000.100.200.300.402-2
Trazar el gráfico f(x)
Respuesta [src] 
       /   2                         \          /   2                           \
RootSum\4*z  + 1, i -> i*log(9 + 2*i)/   RootSum\4*z  + 1, i -> i*log(1/9 + 2*i)/
-------------------------------------- - ----------------------------------------
                log(3)                                    log(3)
−RootSum⁡(4z2+1,(i↦ilog⁡(2i+19)))log⁡(3)+RootSum⁡(4z2+1,(i↦ilog⁡(2i+9)))log⁡(3)- \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \frac{1}{9} \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 9 \right)} \right)\right)}}{\log{\left(3 \right)}} 
=
= 
       /   2                         \          /   2                           \
RootSum\4*z  + 1, i -> i*log(9 + 2*i)/   RootSum\4*z  + 1, i -> i*log(1/9 + 2*i)/
-------------------------------------- - ----------------------------------------
                log(3)                                    log(3)
−RootSum⁡(4z2+1,(i↦ilog⁡(2i+19)))log⁡(3)+RootSum⁡(4z2+1,(i↦ilog⁡(2i+9)))log⁡(3)- \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \frac{1}{9} \right)} \right)\right)}}{\log{\left(3 \right)}} + \frac{\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 9 \right)} \right)\right)}}{\log{\left(3 \right)}} 
RootSum(4*_z^2 + 1, Lambda(_i, _i*log(9 + 2*_i)))/log(3) - RootSum(4*_z^2 + 1, Lambda(_i, _i*log(1/9 + 2*_i)))/log(3)
Respuesta numérica [src] 
0.476600144563355
0.476600144563355

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

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