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Resolución de integrales/ (x)^2/ sin(x)/ xdx/sin(x)^2

Integral de xdx/sin(x)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi           
 --           
 3            
  /           
 |            
 |     x      
 |  ------- dx
 |     2      
 |  sin (x)   
 |            
/             
pi            
--            
4
∫π4π3xsin⁡2(x) dx\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}} \frac{x}{\sin^{2}{\left(x \right)}}\, dx 
Integral(x/sin(x)^2, (x, pi/4, pi/3))
Respuesta (Indefinida) [src] 
  /                                         /x\                         
 |                                     x*tan|-|                         
 |    x                /       2/x\\        \2/      x          /   /x\\
 | ------- dx = C - log|1 + tan |-|| + -------- - -------- + log|tan|-||
 |    2                \        \2//      2            /x\      \   \2//
 | sin (x)                                        2*tan|-|              
 |                                                     \2/              
/
∫xsin⁡2(x) dx=C+xtan⁡(x2)2−x2tan⁡(x2)−log⁡(tan⁡2(x2)+1)+log⁡(tan⁡(x2))\int \frac{x}{\sin^{2}{\left(x \right)}}\, dx = C + \frac{x \tan{\left(\frac{x}{2} \right)}}{2} - \frac{x}{2 \tan{\left(\frac{x}{2} \right)}} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}
Simplificar
Gráfica
0.8000.8250.8500.8750.9000.9250.9500.9751.0001.0255-5
Trazar el gráfico f(x)
Respuesta [src] 
                                 /       ___\        ___                       /  ___\      /                2\
               /       ___\   pi*\-1 + \/ 2 /   pi*\/ 3          pi            |\/ 3 |      |    /       ___\ |
-log(4/3) - log\-1 + \/ 2 / - --------------- - -------- + -------------- + log|-----| + log\1 + \-1 + \/ 2 / /
                                     8             9         /       ___\      \  3  /                         
                                                           8*\-1 + \/ 2 /
−3π9+log⁡(33)−log⁡(43)−π(−1+2)8+log⁡((−1+2)2+1)−log⁡(−1+2)+π8(−1+2)- \frac{\sqrt{3} \pi}{9} + \log{\left(\frac{\sqrt{3}}{3} \right)} - \log{\left(\frac{4}{3} \right)} - \frac{\pi \left(-1 + \sqrt{2}\right)}{8} + \log{\left(\left(-1 + \sqrt{2}\right)^{2} + 1 \right)} - \log{\left(-1 + \sqrt{2} \right)} + \frac{\pi}{8 \left(-1 + \sqrt{2}\right)} 
=
= 
                                 /       ___\        ___                       /  ___\      /                2\
               /       ___\   pi*\-1 + \/ 2 /   pi*\/ 3          pi            |\/ 3 |      |    /       ___\ |
-log(4/3) - log\-1 + \/ 2 / - --------------- - -------- + -------------- + log|-----| + log\1 + \-1 + \/ 2 / /
                                     8             9         /       ___\      \  3  /                         
                                                           8*\-1 + \/ 2 /
−3π9+log⁡(33)−log⁡(43)−π(−1+2)8+log⁡((−1+2)2+1)−log⁡(−1+2)+π8(−1+2)- \frac{\sqrt{3} \pi}{9} + \log{\left(\frac{\sqrt{3}}{3} \right)} - \log{\left(\frac{4}{3} \right)} - \frac{\pi \left(-1 + \sqrt{2}\right)}{8} + \log{\left(\left(-1 + \sqrt{2}\right)^{2} + 1 \right)} - \log{\left(-1 + \sqrt{2} \right)} + \frac{\pi}{8 \left(-1 + \sqrt{2}\right)} 
-log(4/3) - log(-1 + sqrt(2)) - pi*(-1 + sqrt(2))/8 - pi*sqrt(3)/9 + pi/(8*(-1 + sqrt(2))) + log(sqrt(3)/3) + log(1 + (-1 + sqrt(2))^2)
Respuesta numérica [src] 
0.383530929373458
0.383530929373458

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

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