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Resolución de integrales/ tg(x)/ sin²x/ cos²x/ (6+tg(x))/(9sin²x+4cos²x)

Integral de (6+tg(x))/(9sin²x+4cos²x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 atan(2/3)                        
     /                            
    |                             
    |           6 + tan(x)        
    |     --------------------- dx
    |          2           2      
    |     9*sin (x) + 4*cos (x)   
    |                             
   /                              
   0
∫0atan⁡(23)tan⁡(x)+69sin⁡2(x)+4cos⁡2(x) dx\int\limits_{0}^{\operatorname{atan}{\left(\frac{2}{3} \right)}} \frac{\tan{\left(x \right)} + 6}{9 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx 
Integral((6 + tan(x))/(9*sin(x)^2 + 4*cos(x)^2), (x, 0, atan(2/3)))
Respuesta (Indefinida) [src] 
                                            /        /x   pi\       /    ___    /x\  \\            /        /x   pi\       /    ___    /x\  \\                                               /        /x   pi\       /    ___    /x\  \\                                              /        /x   pi\       /    ___    /x\  \\                              
                                            |        |- - --|       |  \/ 2 *tan|-|  ||            |        |- - --|       |  \/ 2 *tan|-|  ||                _____________    _____________ |        |- - --|       |  \/ 2 *tan|-|  ||               _____________    _____________ |        |- - --|       |  \/ 2 *tan|-|  ||                              
                                       ____ |        |2   2 |       |           \2/  ||        ___ |        |2   2 |       |           \2/  ||        ____   /         ___    /         ___  |        |2   2 |       |           \2/  ||        ___   /         ___    /         ___  |        |2   2 |       |           \2/  ||                              
                                  36*\/ 10 *|pi*floor|------| + atan|----------------||   84*\/ 2 *|pi*floor|------| + atan|----------------||   18*\/ 10 *\/  7 - 3*\/ 5  *\/  7 + 3*\/ 5  *|pi*floor|------| + atan|----------------||   42*\/ 2 *\/  7 - 3*\/ 5  *\/  7 + 3*\/ 5  *|pi*floor|------| + atan|----------------||                              
  /                                         |        \  pi  /       |   _____________||            |        \  pi  /       |   _____________||                                               |        \  pi  /       |   _____________||                                              |        \  pi  /       |   _____________||     /                        
 |                                          |                       |  /         ___ ||            |                       |  /         ___ ||                                               |                       |  /         ___ ||                                              |                       |  /         ___ ||    |                         
 |       6 + tan(x)                         \                       \\/  7 - 3*\/ 5  //            \                       \\/  7 - 3*\/ 5  //                                               \                       \\/  7 + 3*\/ 5  //                                              \                       \\/  7 + 3*\/ 5  //    |         tan(x)          
 | --------------------- dx = C + ----------------------------------------------------- + ---------------------------------------------------- + --------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------- +  | --------------------- dx
 |      2           2                       _____________               _____________              _____________               _____________                                _____________               _____________                                                _____________               _____________                       |      2           2      
 | 9*sin (x) + 4*cos (x)                   /         ___         ___   /         ___              /         ___         ___   /         ___                                /         ___         ___   /         ___                                                /         ___         ___   /         ___                        | 4*cos (x) + 9*sin (x)   
 |                                   216*\/  7 - 3*\/ 5   + 96*\/ 5 *\/  7 - 3*\/ 5         216*\/  7 - 3*\/ 5   + 96*\/ 5 *\/  7 - 3*\/ 5                           216*\/  7 - 3*\/ 5   + 96*\/ 5 *\/  7 - 3*\/ 5                                           216*\/  7 - 3*\/ 5   + 96*\/ 5 *\/  7 - 3*\/ 5                         |                         
/                                                                                                                                                                                                                                                                                                                                   /
∫tan⁡(x)+69sin⁡2(x)+4cos⁡2(x) dx=C+3610(atan⁡(2tan⁡(x2)7−35)+π⌊x2−π2π⌋)9657−35+2167−35+842(atan⁡(2tan⁡(x2)7−35)+π⌊x2−π2π⌋)9657−35+2167−35+18107−3535+7(atan⁡(2tan⁡(x2)35+7)+π⌊x2−π2π⌋)9657−35+2167−35+4227−3535+7(atan⁡(2tan⁡(x2)35+7)+π⌊x2−π2π⌋)9657−35+2167−35+∫tan⁡(x)9sin⁡2(x)+4cos⁡2(x) dx\int \frac{\tan{\left(x \right)} + 6}{9 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx = C + \frac{36 \sqrt{10} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{7 - 3 \sqrt{5}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \frac{84 \sqrt{2} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{7 - 3 \sqrt{5}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \frac{18 \sqrt{10} \sqrt{7 - 3 \sqrt{5}} \sqrt{3 \sqrt{5} + 7} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{3 \sqrt{5} + 7}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \frac{42 \sqrt{2} \sqrt{7 - 3 \sqrt{5}} \sqrt{3 \sqrt{5} + 7} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{3 \sqrt{5} + 7}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \int \frac{\tan{\left(x \right)}}{9 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx
Simplificar
Respuesta numérica [src] 
0.823906340095223
0.823906340095223

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

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