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Resolución de integrales/ sin(3*x)/ x/(sin(3*x)*sin(3*x))

Integral de x/(sin(3*x)*sin(3*x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |          x           
 |  ----------------- dx
 |  sin(3*x)*sin(3*x)   
 |                      
/                       
1/5
$$\int\limits_{\frac{1}{5}}^{1} \frac{x}{\sin{\left(3 x \right)} \sin{\left(3 x \right)}}\, dx$$ 
Integral(x/((sin(3*x)*sin(3*x))), (x, 1/5, 1))
Respuesta (Indefinida) [src] 
  /                              /       2/3*x\\      /   /3*x\\                     /3*x\
 |                            log|1 + tan |---||   log|tan|---||                x*tan|---|
 |         x                     \        \ 2 //      \   \ 2 //       x             \ 2 /
 | ----------------- dx = C - ------------------ + ------------- - ---------- + ----------
 | sin(3*x)*sin(3*x)                  9                  9              /3*x\       6     
 |                                                                 6*tan|---|             
/                                                                       \ 2 /
$$\int \frac{x}{\sin{\left(3 x \right)} \sin{\left(3 x \right)}}\, dx = C + \frac{x \tan{\left(\frac{3 x}{2} \right)}}{6} - \frac{x}{6 \tan{\left(\frac{3 x}{2} \right)}} - \frac{\log{\left(\tan^{2}{\left(\frac{3 x}{2} \right)} + 1 \right)}}{9} + \frac{\log{\left(\tan{\left(\frac{3 x}{2} \right)} \right)}}{9}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                  /       2     \                                              /       2      \                               
      1        log\1 + tan (3/2)/   log(tan(3/10))   tan(3/10)   tan(3/2)   log\1 + tan (3/10)/   log(tan(3/2))        1      
- ---------- - ------------------ - -------------- - --------- + -------- + ------------------- + ------------- + ------------
  6*tan(3/2)           9                  9              30         6                9                  9         30*tan(3/10)
$$- \frac{\log{\left(1 + \tan^{2}{\left(\frac{3}{2} \right)} \right)}}{9} - \frac{1}{6 \tan{\left(\frac{3}{2} \right)}} - \frac{\tan{\left(\frac{3}{10} \right)}}{30} + \frac{\log{\left(\tan^{2}{\left(\frac{3}{10} \right)} + 1 \right)}}{9} + \frac{1}{30 \tan{\left(\frac{3}{10} \right)}} - \frac{\log{\left(\tan{\left(\frac{3}{10} \right)} \right)}}{9} + \frac{\log{\left(\tan{\left(\frac{3}{2} \right)} \right)}}{9} + \frac{\tan{\left(\frac{3}{2} \right)}}{6}$$ 
=
= 
                  /       2     \                                              /       2      \                               
      1        log\1 + tan (3/2)/   log(tan(3/10))   tan(3/10)   tan(3/2)   log\1 + tan (3/10)/   log(tan(3/2))        1      
- ---------- - ------------------ - -------------- - --------- + -------- + ------------------- + ------------- + ------------
  6*tan(3/2)           9                  9              30         6                9                  9         30*tan(3/10)
$$- \frac{\log{\left(1 + \tan^{2}{\left(\frac{3}{2} \right)} \right)}}{9} - \frac{1}{6 \tan{\left(\frac{3}{2} \right)}} - \frac{\tan{\left(\frac{3}{10} \right)}}{30} + \frac{\log{\left(\tan^{2}{\left(\frac{3}{10} \right)} + 1 \right)}}{9} + \frac{1}{30 \tan{\left(\frac{3}{10} \right)}} - \frac{\log{\left(\tan{\left(\frac{3}{10} \right)} \right)}}{9} + \frac{\log{\left(\tan{\left(\frac{3}{2} \right)} \right)}}{9} + \frac{\tan{\left(\frac{3}{2} \right)}}{6}$$ 
-1/(6*tan(3/2)) - log(1 + tan(3/2)^2)/9 - log(tan(3/10))/9 - tan(3/10)/30 + tan(3/2)/6 + log(1 + tan(3/10)^2)/9 + log(tan(3/2))/9 + 1/(30*tan(3/10))
Respuesta numérica [src] 
2.28179923683597
2.28179923683597

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

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