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Resolución de integrales/ arctg/ 2^(-x)/ 2^(-x)*arctg2^x

Integral de 2^(-x)*arctg2^x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |   -x     x      
 |  2  *atan (2) dx
 |                 
/                  
0
∫012−xatan⁡x(2) dx\int\limits_{0}^{1} 2^{- x} \operatorname{atan}^{x}{\left(2 \right)}\, dx 
Integral(2^(-x)*atan(2)^x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                 
 |                                     x            
 |  -x     x                       atan (2)         
 | 2  *atan (2) dx = C - ---------------------------
 |                        x           x             
/                        2 *log(2) - 2 *log(atan(2))
∫2−xatan⁡x(2) dx=C−atan⁡x(2)−2xlog⁡(atan⁡(2))+2xlog⁡(2)\int 2^{- x} \operatorname{atan}^{x}{\left(2 \right)}\, dx = C - \frac{\operatorname{atan}^{x}{\left(2 \right)}}{- 2^{x} \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + 2^{x} \log{\left(2 \right)}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Trazar el gráfico f(x)
Respuesta [src] 
          1                       atan(2)          
---------------------- - --------------------------
-log(atan(2)) + log(2)   -2*log(atan(2)) + 2*log(2)
−atan⁡(2)−2log⁡(atan⁡(2))+2log⁡(2)+1−log⁡(atan⁡(2))+log⁡(2)- \frac{\operatorname{atan}{\left(2 \right)}}{- 2 \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + 2 \log{\left(2 \right)}} + \frac{1}{- \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + \log{\left(2 \right)}} 
=
= 
          1                       atan(2)          
---------------------- - --------------------------
-log(atan(2)) + log(2)   -2*log(atan(2)) + 2*log(2)
−atan⁡(2)−2log⁡(atan⁡(2))+2log⁡(2)+1−log⁡(atan⁡(2))+log⁡(2)- \frac{\operatorname{atan}{\left(2 \right)}}{- 2 \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + 2 \log{\left(2 \right)}} + \frac{1}{- \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + \log{\left(2 \right)}} 
1/(-log(atan(2)) + log(2)) - atan(2)/(-2*log(atan(2)) + 2*log(2))
Respuesta numérica [src] 
0.754914519904385
0.754914519904385

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

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