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Resolución de integrales/ (x)^2/ tan(x)/ tan(x)^2/(1+tan(x)^2)

Integral de tan(x)^2/(1+tan(x)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |       2        
 |    tan (x)     
 |  ----------- dx
 |         2      
 |  1 + tan (x)   
 |                
/                 
0
∫01tan⁡2(x)tan⁡2(x)+1 dx\int\limits_{0}^{1} \frac{\tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\, dx 
Integral(tan(x)^2/(1 + tan(x)^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                  
 |                                                                   
 |      2                                                      2     
 |   tan (x)                  x             tan(x)        x*tan (x)  
 | ----------- dx = C + ------------- - ------------- + -------------
 |        2                      2               2               2   
 | 1 + tan (x)          2 + 2*tan (x)   2 + 2*tan (x)   2 + 2*tan (x)
 |                                                                   
/
∫tan⁡2(x)tan⁡2(x)+1 dx=C+xtan⁡2(x)2tan⁡2(x)+2+x2tan⁡2(x)+2−tan⁡(x)2tan⁡2(x)+2\int \frac{\tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\, dx = C + \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} + \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Trazar el gráfico f(x)
Respuesta [src] 
                      2                      
      1            tan (1)          tan(1)   
------------- + ------------- - -------------
         2               2               2   
2 + 2*tan (1)   2 + 2*tan (1)   2 + 2*tan (1)
−tan⁡(1)2+2tan⁡2(1)+12+2tan⁡2(1)+tan⁡2(1)2+2tan⁡2(1)- \frac{\tan{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{1}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan^{2}{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} 
=
= 
                      2                      
      1            tan (1)          tan(1)   
------------- + ------------- - -------------
         2               2               2   
2 + 2*tan (1)   2 + 2*tan (1)   2 + 2*tan (1)
−tan⁡(1)2+2tan⁡2(1)+12+2tan⁡2(1)+tan⁡2(1)2+2tan⁡2(1)- \frac{\tan{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{1}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan^{2}{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} 
1/(2 + 2*tan(1)^2) + tan(1)^2/(2 + 2*tan(1)^2) - tan(1)/(2 + 2*tan(1)^2)
Respuesta numérica [src] 
0.27267564329358
0.27267564329358

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

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