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Resolución de integrales/ cos^2/ sin^2/ dx/(3sin^2(x)+4cos^2(x))

Integral de dx/(3sin^2(x)+4cos^2(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |            1             
 |  --------------------- dx
 |       2           2      
 |  3*sin (x) + 4*cos (x)   
 |                          
/                           
0
∫0113sin⁡2(x)+4cos⁡2(x) dx\int\limits_{0}^{1} \frac{1}{3 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx 
Integral(1/(3*sin(x)^2 + 4*cos(x)^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                        /        /x   pi\       /              ___    /x\\\         /        /x   pi\       /            ___    /x\\\
                                        |        |- - --|       |    ___   2*\/ 3 *tan|-|||         |        |- - --|       |  ___   2*\/ 3 *tan|-|||
  /                                 ___ |        |2   2 |       |  \/ 3               \2/||     ___ |        |2   2 |       |\/ 3               \2/||
 |                                \/ 3 *|pi*floor|------| + atan|- ----- + --------------||   \/ 3 *|pi*floor|------| + atan|----- + --------------||
 |           1                          \        \  pi  /       \    3           3       //         \        \  pi  /       \  3           3       //
 | --------------------- dx = C + --------------------------------------------------------- + -------------------------------------------------------
 |      2           2                                         6                                                          6                           
 | 3*sin (x) + 4*cos (x)                                                                                                                             
 |                                                                                                                                                   
/
∫13sin⁡2(x)+4cos⁡2(x) dx=C+3(atan⁡(23tan⁡(x2)3−33)+π⌊x2−π2π⌋)6+3(atan⁡(23tan⁡(x2)3+33)+π⌊x2−π2π⌋)6\int \frac{1}{3 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx = C + \frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} - \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6} + \frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Trazar el gráfico f(x)
Respuesta [src] 
                 /          /  ___       ___         \\         /          /  ___       ___         \\
             ___ |          |\/ 3    2*\/ 3 *tan(1/2)||     ___ |          |\/ 3    2*\/ 3 *tan(1/2)||
     ___   \/ 3 *|-pi - atan|----- - ----------------||   \/ 3 *|-pi + atan|----- + ----------------||
pi*\/ 3          \          \  3            3        //         \          \  3            3        //
-------- + -------------------------------------------- + --------------------------------------------
   3                            6                                              6
3(−π−atan⁡(−23tan⁡(12)3+33))6+3(−π+atan⁡(33+23tan⁡(12)3))6+3π3\frac{\sqrt{3} \left(- \pi - \operatorname{atan}{\left(- \frac{2 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)}\right)}{6} + \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{6} + \frac{\sqrt{3} \pi}{3} 
=
= 
                 /          /  ___       ___         \\         /          /  ___       ___         \\
             ___ |          |\/ 3    2*\/ 3 *tan(1/2)||     ___ |          |\/ 3    2*\/ 3 *tan(1/2)||
     ___   \/ 3 *|-pi - atan|----- - ----------------||   \/ 3 *|-pi + atan|----- + ----------------||
pi*\/ 3          \          \  3            3        //         \          \  3            3        //
-------- + -------------------------------------------- + --------------------------------------------
   3                            6                                              6
3(−π−atan⁡(−23tan⁡(12)3+33))6+3(−π+atan⁡(33+23tan⁡(12)3))6+3π3\frac{\sqrt{3} \left(- \pi - \operatorname{atan}{\left(- \frac{2 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)}\right)}{6} + \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{6} + \frac{\sqrt{3} \pi}{3} 
pi*sqrt(3)/3 + sqrt(3)*(-pi - atan(sqrt(3)/3 - 2*sqrt(3)*tan(1/2)/3))/6 + sqrt(3)*(-pi + atan(sqrt(3)/3 + 2*sqrt(3)*tan(1/2)/3))/6
Respuesta numérica [src] 
0.26927791049623
0.26927791049623

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

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