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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                          
  /                          
 |                           
 |          tan(x)           
 |  ---------------------- dx
 |     2                     
 |  tan (x) + 4*tan(x) + 4   
 |                           
/                            
0
∫01tan⁡(x)(tan⁡2(x)+4tan⁡(x))+4 dx\int\limits_{0}^{1} \frac{\tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)}\right) + 4}\, dx 
Integral(tan(x)/(tan(x)^2 + 4*tan(x) + 4), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                    
 |                                                                             /       2   \                                                     /       2   \                         
 |         tan(x)                         20         12*log(2 + tan(x))   6*log\1 + tan (x)/         16*x        6*log(2 + tan(x))*tan(x)   3*log\1 + tan (x)/*tan(x)      8*x*tan(x)  
 | ---------------------- dx = C + --------------- - ------------------ + ------------------ + --------------- - ------------------------ + ------------------------- + ---------------
 |    2                            100 + 50*tan(x)    100 + 50*tan(x)      100 + 50*tan(x)     100 + 50*tan(x)       100 + 50*tan(x)             100 + 50*tan(x)        100 + 50*tan(x)
 | tan (x) + 4*tan(x) + 4                                                                                                                                                              
 |                                                                                                                                                                                     
/
∫tan⁡(x)(tan⁡2(x)+4tan⁡(x))+4 dx=C+8xtan⁡(x)50tan⁡(x)+100+16x50tan⁡(x)+100−6log⁡(tan⁡(x)+2)tan⁡(x)50tan⁡(x)+100−12log⁡(tan⁡(x)+2)50tan⁡(x)+100+3log⁡(tan⁡2(x)+1)tan⁡(x)50tan⁡(x)+100+6log⁡(tan⁡2(x)+1)50tan⁡(x)+100+2050tan⁡(x)+100\int \frac{\tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)}\right) + 4}\, dx = C + \frac{8 x \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} + \frac{16 x}{50 \tan{\left(x \right)} + 100} - \frac{6 \log{\left(\tan{\left(x \right)} + 2 \right)} \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} - \frac{12 \log{\left(\tan{\left(x \right)} + 2 \right)}}{50 \tan{\left(x \right)} + 100} + \frac{3 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} + \frac{6 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{50 \tan{\left(x \right)} + 100} + \frac{20}{50 \tan{\left(x \right)} + 100}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.00.2
Trazar el gráfico f(x)
Respuesta [src] 
                                                             /       2   \                                                     /       2   \       
  1          36         3*log(2)   12*log(2 + tan(1))   6*log\1 + tan (1)/       8*tan(1)      6*log(2 + tan(1))*tan(1)   3*log\1 + tan (1)/*tan(1)
- - + --------------- + -------- - ------------------ + ------------------ + --------------- - ------------------------ + -------------------------
  5   100 + 50*tan(1)      25       100 + 50*tan(1)      100 + 50*tan(1)     100 + 50*tan(1)       100 + 50*tan(1)             100 + 50*tan(1)
−15−12log⁡(tan⁡(1)+2)50tan⁡(1)+100−6log⁡(tan⁡(1)+2)tan⁡(1)50tan⁡(1)+100+3log⁡(1+tan⁡2(1))tan⁡(1)50tan⁡(1)+100+6log⁡(1+tan⁡2(1))50tan⁡(1)+100+8tan⁡(1)50tan⁡(1)+100+3log⁡(2)25+3650tan⁡(1)+100- \frac{1}{5} - \frac{12 \log{\left(\tan{\left(1 \right)} + 2 \right)}}{50 \tan{\left(1 \right)} + 100} - \frac{6 \log{\left(\tan{\left(1 \right)} + 2 \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{6 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{8 \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(2 \right)}}{25} + \frac{36}{50 \tan{\left(1 \right)} + 100} 
=
= 
                                                             /       2   \                                                     /       2   \       
  1          36         3*log(2)   12*log(2 + tan(1))   6*log\1 + tan (1)/       8*tan(1)      6*log(2 + tan(1))*tan(1)   3*log\1 + tan (1)/*tan(1)
- - + --------------- + -------- - ------------------ + ------------------ + --------------- - ------------------------ + -------------------------
  5   100 + 50*tan(1)      25       100 + 50*tan(1)      100 + 50*tan(1)     100 + 50*tan(1)       100 + 50*tan(1)             100 + 50*tan(1)
−15−12log⁡(tan⁡(1)+2)50tan⁡(1)+100−6log⁡(tan⁡(1)+2)tan⁡(1)50tan⁡(1)+100+3log⁡(1+tan⁡2(1))tan⁡(1)50tan⁡(1)+100+6log⁡(1+tan⁡2(1))50tan⁡(1)+100+8tan⁡(1)50tan⁡(1)+100+3log⁡(2)25+3650tan⁡(1)+100- \frac{1}{5} - \frac{12 \log{\left(\tan{\left(1 \right)} + 2 \right)}}{50 \tan{\left(1 \right)} + 100} - \frac{6 \log{\left(\tan{\left(1 \right)} + 2 \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{6 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{8 \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(2 \right)}}{25} + \frac{36}{50 \tan{\left(1 \right)} + 100} 
-1/5 + 36/(100 + 50*tan(1)) + 3*log(2)/25 - 12*log(2 + tan(1))/(100 + 50*tan(1)) + 6*log(1 + tan(1)^2)/(100 + 50*tan(1)) + 8*tan(1)/(100 + 50*tan(1)) - 6*log(2 + tan(1))*tan(1)/(100 + 50*tan(1)) + 3*log(1 + tan(1)^2)*tan(1)/(100 + 50*tan(1))
Respuesta numérica [src] 
0.0772104113509897
0.0772104113509897

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

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