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Resolución de integrales/ tgx^2/ 1/(А-tgx^2)(1/2)

Integral de 1/(А-tgx^2)(1/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |  /       2   \     
 |  \a - tan (x)/*2   
 |                    
/                     
0
∫0112(a−tan⁡2(x)) dx\int\limits_{0}^{1} \frac{1}{2 \left(a - \tan^{2}{\left(x \right)}\right)}\, dx 
Integral(1/((a - tan(x)^2)*2), (x, 0, 1))
Solución detallada

  1. La integral del producto de una función por una constante es la constante por la integral de esta función:

    ∫12(a−tan⁡2(x)) dx=∫1a−tan⁡2(x) dx2\int \frac{1}{2 \left(a - \tan^{2}{\left(x \right)}\right)}\, dx = \frac{\int \frac{1}{a - \tan^{2}{\left(x \right)}}\, dx}{2}

    1. No puedo encontrar los pasos en la búsqueda de esta integral.

      Pero la integral

      {−xtan⁡2(x)2tan⁡2(x)+2−x2tan⁡2(x)+2−tan⁡(x)2tan⁡2(x)+2for a=−1x+1tan⁡(x)for a=02a52x2a72+6a52+6a32+2a+4a32x2a72+6a52+6a32+2a+2ax2a72+6a52+6a32+2a−a2log⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+a2log⁡(a+tan⁡(x))2a72+6a52+6a32+2a−2alog⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+2alog⁡(a+tan⁡(x))2a72+6a52+6a32+2a−log⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+log⁡(a+tan⁡(x))2a72+6a52+6a32+2aotherwese\begin{cases} - \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} - \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} & \text{for}\: a = -1 \\x + \frac{1}{\tan{\left(x \right)}} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{4 a^{\frac{3}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 \sqrt{a} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{\log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} & \text{otherwese} \end{cases}

    Por lo tanto, el resultado es: {−xtan⁡2(x)2tan⁡2(x)+2−x2tan⁡2(x)+2−tan⁡(x)2tan⁡2(x)+2for a=−1x+1tan⁡(x)for a=02a52x2a72+6a52+6a32+2a+4a32x2a72+6a52+6a32+2a+2ax2a72+6a52+6a32+2a−a2log⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+a2log⁡(a+tan⁡(x))2a72+6a52+6a32+2a−2alog⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+2alog⁡(a+tan⁡(x))2a72+6a52+6a32+2a−log⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+log⁡(a+tan⁡(x))2a72+6a52+6a32+2aotherwese2\frac{\begin{cases} - \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} - \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} & \text{for}\: a = -1 \\x + \frac{1}{\tan{\left(x \right)}} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{4 a^{\frac{3}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 \sqrt{a} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{\log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} & \text{otherwese} \end{cases}}{2}

  2. Ahora simplificar:

    {−2x+sin⁡(2x)8for a=−1x+1tan⁡(x)2for a=02a52x+4a32x+2ax−a2log⁡(−a+tan⁡(x))+a2log⁡(a+tan⁡(x))−2alog⁡(−a+tan⁡(x))+2alog⁡(a+tan⁡(x))−log⁡(−a+tan⁡(x))+log⁡(a+tan⁡(x))4a(a+1)3otherwese\begin{cases} - \frac{2 x + \sin{\left(2 x \right)}}{8} & \text{for}\: a = -1 \\\frac{x + \frac{1}{\tan{\left(x \right)}}}{2} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x + 4 a^{\frac{3}{2}} x + 2 \sqrt{a} x - a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - 2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + 2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{4 \sqrt{a} \left(a + 1\right)^{3}} & \text{otherwese} \end{cases}

  3. Añadimos la constante de integración:

    {−2x+sin⁡(2x)8for a=−1x+1tan⁡(x)2for a=02a52x+4a32x+2ax−a2log⁡(−a+tan⁡(x))+a2log⁡(a+tan⁡(x))−2alog⁡(−a+tan⁡(x))+2alog⁡(a+tan⁡(x))−log⁡(−a+tan⁡(x))+log⁡(a+tan⁡(x))4a(a+1)3otherwese+constant\begin{cases} - \frac{2 x + \sin{\left(2 x \right)}}{8} & \text{for}\: a = -1 \\\frac{x + \frac{1}{\tan{\left(x \right)}}}{2} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x + 4 a^{\frac{3}{2}} x + 2 \sqrt{a} x - a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - 2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + 2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{4 \sqrt{a} \left(a + 1\right)^{3}} & \text{otherwese} \end{cases}+ \mathrm{constant}

Respuesta:

{−2x+sin⁡(2x)8for a=−1x+1tan⁡(x)2for a=02a52x+4a32x+2ax−a2log⁡(−a+tan⁡(x))+a2log⁡(a+tan⁡(x))−2alog⁡(−a+tan⁡(x))+2alog⁡(a+tan⁡(x))−log⁡(−a+tan⁡(x))+log⁡(a+tan⁡(x))4a(a+1)3otherwese+constant\begin{cases} - \frac{2 x + \sin{\left(2 x \right)}}{8} & \text{for}\: a = -1 \\\frac{x + \frac{1}{\tan{\left(x \right)}}}{2} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x + 4 a^{\frac{3}{2}} x + 2 \sqrt{a} x - a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - 2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + 2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{4 \sqrt{a} \left(a + 1\right)^{3}} & \text{otherwese} \end{cases}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
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                            |                                                                                                                                                     x             tan(x)        x*tan (x)                                                                                                                                                            
                            |                                                                                                                                             - ------------- - ------------- - -------------                                                                                                                                                for a = -1
                            |                                                                                                                                                        2               2               2                                                                                                                                                             
                            |                                                                                                                                               2 + 2*tan (x)   2 + 2*tan (x)   2 + 2*tan (x)                                                                                                                                                          
                            |                                                                                                                                                                                                                                                                                                                                                      
                            |                                                                                                                                                                      1                                                                                                                                                                               
                            <                                                                                                                                                                x + ------                                                                                                                                                                  for a = 0 
                            |                                                                                                                                                                    tan(x)                                                                                                                                                                            
                            |                                                                                                                                                                                                                                                                                                                                                      
                            |          /  ___         \                    /    ___         \                 2    /  ___         \               2    /    ___         \                   /    ___         \                    /  ___         \                           ___                                  5/2                                  3/2                         
                            |       log\\/ a  + tan(x)/                 log\- \/ a  + tan(x)/                a *log\\/ a  + tan(x)/              a *log\- \/ a  + tan(x)/            2*a*log\- \/ a  + tan(x)/             2*a*log\\/ a  + tan(x)/                     2*x*\/ a                              2*x*a                                4*x*a                            
  /                         |---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - ---------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- + ----------------------------------  otherwise 
 |                          |    ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2            
 |        1                 \2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a               
 | --------------- dx = C + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 | /       2   \                                                                                                                                                                                       2                                                                                                                                                                           
 | \a - tan (x)/*2                                                                                                                                                                                                                                                                                                                                                                 
 |                                                                                                                                                                                                                                                                                                                                                                                 
/
∫12(a−tan⁡2(x)) dx=C+{−xtan⁡2(x)2tan⁡2(x)+2−x2tan⁡2(x)+2−tan⁡(x)2tan⁡2(x)+2for a=−1x+1tan⁡(x)for a=02a52x2a72+6a52+6a32+2a+4a32x2a72+6a52+6a32+2a+2ax2a72+6a52+6a32+2a−a2log⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+a2log⁡(a+tan⁡(x))2a72+6a52+6a32+2a−2alog⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+2alog⁡(a+tan⁡(x))2a72+6a52+6a32+2a−log⁡(−a+tan⁡(x))2a72+6a52+6a32+2a+log⁡(a+tan⁡(x))2a72+6a52+6a32+2aotherwise2\int \frac{1}{2 \left(a - \tan^{2}{\left(x \right)}\right)}\, dx = C + \frac{\begin{cases} - \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} - \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} & \text{for}\: a = -1 \\x + \frac{1}{\tan{\left(x \right)}} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{4 a^{\frac{3}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 \sqrt{a} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{\log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} & \text{otherwise} \end{cases}}{2}
Simplificar
Respuesta [src] 
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|                                                                                                                                                                                                                                                                                1                tan (1)              tan(1)                                                                                                                                                                                                                                                                                        
|                                                                                                                                                                                                                                                                      - ----------------- - ----------------- - -----------------                                                                                                                                                                                                                                                                         for a = -1
|                                                                                                                                                                                                                                                                          /         2   \     /         2   \     /         2   \                                                                                                                                                                                                                                                                                   
|                                                                                                                                                                                                                                                                        2*\2 + 2*tan (1)/   2*\2 + 2*tan (1)/   2*\2 + 2*tan (1)/                                                                                                                                                                                                                                                                                   
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
<                                                                                                                                                                                                                                                                                                  -oo                                                                                                                                                                                                                                                                                                     for a = 0 
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
|                ___                                  5/2                                  /   ___\                             /  ___         \                              3/2                                  /  ___\                            /    ___         \                           /   ___\                         /  ___         \                       2    /   ___\                        2    /  ___         \                           /  ___\                        /    ___         \                      2    /  ___\                        2    /    ___         \                   
|              \/ a                                  a                                  log\-\/ a /                          log\\/ a  + tan(1)/                           2*a                                  log\\/ a /                         log\- \/ a  + tan(1)/                      a*log\-\/ a /                    a*log\\/ a  + tan(1)/                      a *log\-\/ a /                       a *log\\/ a  + tan(1)/                      a*log\\/ a /                   a*log\- \/ a  + tan(1)/                     a *log\\/ a /                       a *log\- \/ a  + tan(1)/                   
|---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- + ---------------------------------- - -------------------------------------- - -------------------------------------- + ---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- - ---------------------------------- - ---------------------------------- - -------------------------------------- - --------------------------------------  otherwise 
|    ___      7/2      3/2      5/2       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\            
\2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /
{−tan⁡2(1)2(2+2tan⁡2(1))−tan⁡(1)2(2+2tan⁡2(1))−12(2+2tan⁡2(1))for a=−1−∞for a=0a522a72+6a52+6a32+2a+2a322a72+6a52+6a32+2a+a2a72+6a52+6a32+2a+a2log⁡(−a)2(2a72+6a52+6a32+2a)−a2log⁡(a)2(2a72+6a52+6a32+2a)−a2log⁡(−a+tan⁡(1))2(2a72+6a52+6a32+2a)+a2log⁡(a+tan⁡(1))2(2a72+6a52+6a32+2a)+alog⁡(−a)2a72+6a52+6a32+2a−alog⁡(a)2a72+6a52+6a32+2a−alog⁡(−a+tan⁡(1))2a72+6a52+6a32+2a+alog⁡(a+tan⁡(1))2a72+6a52+6a32+2a+log⁡(−a)2(2a72+6a52+6a32+2a)−log⁡(a)2(2a72+6a52+6a32+2a)−log⁡(−a+tan⁡(1))2(2a72+6a52+6a32+2a)+log⁡(a+tan⁡(1))2(2a72+6a52+6a32+2a)otherwise\begin{cases} - \frac{\tan^{2}{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{\tan{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{1}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} & \text{for}\: a = -1 \\-\infty & \text{for}\: a = 0 \\\frac{a^{\frac{5}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a^{\frac{3}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\sqrt{a}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a \log{\left(- \sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(\sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{\log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} & \text{otherwise} \end{cases} 
=
= 
/                                                                                                                                                                                                                                                                                                    2                                                                                                                                                                                                                                                                                                               
|                                                                                                                                                                                                                                                                                1                tan (1)              tan(1)                                                                                                                                                                                                                                                                                        
|                                                                                                                                                                                                                                                                      - ----------------- - ----------------- - -----------------                                                                                                                                                                                                                                                                         for a = -1
|                                                                                                                                                                                                                                                                          /         2   \     /         2   \     /         2   \                                                                                                                                                                                                                                                                                   
|                                                                                                                                                                                                                                                                        2*\2 + 2*tan (1)/   2*\2 + 2*tan (1)/   2*\2 + 2*tan (1)/                                                                                                                                                                                                                                                                                   
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
<                                                                                                                                                                                                                                                                                                  -oo                                                                                                                                                                                                                                                                                                     for a = 0 
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
|                ___                                  5/2                                  /   ___\                             /  ___         \                              3/2                                  /  ___\                            /    ___         \                           /   ___\                         /  ___         \                       2    /   ___\                        2    /  ___         \                           /  ___\                        /    ___         \                      2    /  ___\                        2    /    ___         \                   
|              \/ a                                  a                                  log\-\/ a /                          log\\/ a  + tan(1)/                           2*a                                  log\\/ a /                         log\- \/ a  + tan(1)/                      a*log\-\/ a /                    a*log\\/ a  + tan(1)/                      a *log\-\/ a /                       a *log\\/ a  + tan(1)/                      a*log\\/ a /                   a*log\- \/ a  + tan(1)/                     a *log\\/ a /                       a *log\- \/ a  + tan(1)/                   
|---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- + ---------------------------------- - -------------------------------------- - -------------------------------------- + ---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- - ---------------------------------- - ---------------------------------- - -------------------------------------- - --------------------------------------  otherwise 
|    ___      7/2      3/2      5/2       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\       ___      7/2      3/2      5/2       ___      7/2      3/2      5/2     /    ___      7/2      3/2      5/2\     /    ___      7/2      3/2      5/2\            
\2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\/ a  + 2*a    + 6*a    + 6*a      2*\/ a  + 2*a    + 6*a    + 6*a      2*\2*\/ a  + 2*a    + 6*a    + 6*a   /   2*\2*\/ a  + 2*a    + 6*a    + 6*a   /
{−tan⁡2(1)2(2+2tan⁡2(1))−tan⁡(1)2(2+2tan⁡2(1))−12(2+2tan⁡2(1))for a=−1−∞for a=0a522a72+6a52+6a32+2a+2a322a72+6a52+6a32+2a+a2a72+6a52+6a32+2a+a2log⁡(−a)2(2a72+6a52+6a32+2a)−a2log⁡(a)2(2a72+6a52+6a32+2a)−a2log⁡(−a+tan⁡(1))2(2a72+6a52+6a32+2a)+a2log⁡(a+tan⁡(1))2(2a72+6a52+6a32+2a)+alog⁡(−a)2a72+6a52+6a32+2a−alog⁡(a)2a72+6a52+6a32+2a−alog⁡(−a+tan⁡(1))2a72+6a52+6a32+2a+alog⁡(a+tan⁡(1))2a72+6a52+6a32+2a+log⁡(−a)2(2a72+6a52+6a32+2a)−log⁡(a)2(2a72+6a52+6a32+2a)−log⁡(−a+tan⁡(1))2(2a72+6a52+6a32+2a)+log⁡(a+tan⁡(1))2(2a72+6a52+6a32+2a)otherwise\begin{cases} - \frac{\tan^{2}{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{\tan{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{1}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} & \text{for}\: a = -1 \\-\infty & \text{for}\: a = 0 \\\frac{a^{\frac{5}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a^{\frac{3}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\sqrt{a}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a \log{\left(- \sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(\sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{\log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} & \text{otherwise} \end{cases} 
Piecewise((-1/(2*(2 + 2*tan(1)^2)) - tan(1)^2/(2*(2 + 2*tan(1)^2)) - tan(1)/(2*(2 + 2*tan(1)^2)), a = -1), (-oo, a = 0), (sqrt(a)/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + a^(5/2)/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + log(-sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + log(sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + 2*a^(3/2)/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) - log(sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) - log(-sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + a*log(-sqrt(a))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + a*log(sqrt(a) + tan(1))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + a^2*log(-sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + a^2*log(sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) - a*log(sqrt(a))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) - a*log(-sqrt(a) + tan(1))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) - a^2*log(sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) - a^2*log(-sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))), True))

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

    © Sr Examen – Калькулятор