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Resolución de integrales/ cos^2/ 3+sinx/ cos^2(x)/(3+sinx)

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |      2        
 |   cos (x)     
 |  ---------- dx
 |  3 + sin(x)   
 |               
/                
0
∫01cos⁡2(x)sin⁡(x)+3 dx\int\limits_{0}^{1} \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 3}\, dx 
Integral(cos(x)^2/(3 + sin(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                           /        /x   pi\       /            ___    /x\\\                                 /        /x   pi\       /            ___    /x\\\
  /                                                        |        |- - --|       |  ___   3*\/ 2 *tan|-|||                                 |        |- - --|       |  ___   3*\/ 2 *tan|-|||
 |                                                     ___ |        |2   2 |       |\/ 2               \2/||          2/x\       ___    2/x\ |        |2   2 |       |\/ 2               \2/||
 |     2                                           4*\/ 2 *|pi*floor|------| + atan|----- + --------------||   3*x*tan |-|   4*\/ 2 *tan |-|*|pi*floor|------| + atan|----- + --------------||
 |  cos (x)                 2            3*x               \        \  pi  /       \  4           4       //           \2/               \2/ \        \  pi  /       \  4           4       //
 | ---------- dx = C + ----------- + ----------- - --------------------------------------------------------- + ----------- - -----------------------------------------------------------------
 | 3 + sin(x)                 2/x\          2/x\                                 2/x\                                 2/x\                                     2/x\                           
 |                     1 + tan |-|   1 + tan |-|                          1 + tan |-|                          1 + tan |-|                              1 + tan |-|                           
/                              \2/           \2/                                  \2/                                  \2/                                      \2/
∫cos⁡2(x)sin⁡(x)+3 dx=C+3xtan⁡2(x2)tan⁡2(x2)+1+3xtan⁡2(x2)+1−42(atan⁡(32tan⁡(x2)4+24)+π⌊x2−π2π⌋)tan⁡2(x2)tan⁡2(x2)+1−42(atan⁡(32tan⁡(x2)4+24)+π⌊x2−π2π⌋)tan⁡2(x2)+1+2tan⁡2(x2)+1\int \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 3}\, dx = C + \frac{3 x \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{3 x}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90020
Trazar el gráfico f(x)
Respuesta [src] 
                                                                           /          /  ___       ___         \\                     /          /  ___       ___         \\
                                                                       ___ |          |\/ 2    3*\/ 2 *tan(1/2)||       ___    2      |          |\/ 2    3*\/ 2 *tan(1/2)||
                           2                 /          /  ___\\   4*\/ 2 *|-pi + atan|----- + ----------------||   4*\/ 2 *tan (1/2)*|-pi + atan|----- + ----------------||
           5          3*tan (1/2)        ___ |          |\/ 2 ||           \          \  4            4        //                     \          \  4            4        //
-2 + ------------- + ------------- + 4*\/ 2 *|-pi + atan|-----|| - ---------------------------------------------- - --------------------------------------------------------
            2               2                \          \  4  //                          2                                                     2                           
     1 + tan (1/2)   1 + tan (1/2)                                                 1 + tan (1/2)                                         1 + tan (1/2)
42(−π+atan⁡(24))−2+3tan⁡2(12)tan⁡2(12)+1−42(−π+atan⁡(24+32tan⁡(12)4))tan⁡2(12)tan⁡2(12)+1+5tan⁡2(12)+1−42(−π+atan⁡(24+32tan⁡(12)4))tan⁡2(12)+14 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right) - 2 + \frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right) \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{5}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right)}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} 
=
= 
                                                                           /          /  ___       ___         \\                     /          /  ___       ___         \\
                                                                       ___ |          |\/ 2    3*\/ 2 *tan(1/2)||       ___    2      |          |\/ 2    3*\/ 2 *tan(1/2)||
                           2                 /          /  ___\\   4*\/ 2 *|-pi + atan|----- + ----------------||   4*\/ 2 *tan (1/2)*|-pi + atan|----- + ----------------||
           5          3*tan (1/2)        ___ |          |\/ 2 ||           \          \  4            4        //                     \          \  4            4        //
-2 + ------------- + ------------- + 4*\/ 2 *|-pi + atan|-----|| - ---------------------------------------------- - --------------------------------------------------------
            2               2                \          \  4  //                          2                                                     2                           
     1 + tan (1/2)   1 + tan (1/2)                                                 1 + tan (1/2)                                         1 + tan (1/2)
42(−π+atan⁡(24))−2+3tan⁡2(12)tan⁡2(12)+1−42(−π+atan⁡(24+32tan⁡(12)4))tan⁡2(12)tan⁡2(12)+1+5tan⁡2(12)+1−42(−π+atan⁡(24+32tan⁡(12)4))tan⁡2(12)+14 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right) - 2 + \frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right) \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{5}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right)}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} 
-2 + 5/(1 + tan(1/2)^2) + 3*tan(1/2)^2/(1 + tan(1/2)^2) + 4*sqrt(2)*(-pi + atan(sqrt(2)/4)) - 4*sqrt(2)*(-pi + atan(sqrt(2)/4 + 3*sqrt(2)*tan(1/2)/4))/(1 + tan(1/2)^2) - 4*sqrt(2)*tan(1/2)^2*(-pi + atan(sqrt(2)/4 + 3*sqrt(2)*tan(1/2)/4))/(1 + tan(1/2)^2)
Respuesta numérica [src] 
0.215837913371703
0.215837913371703

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

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