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Resolución de integrales/ tg^22x

Integral de tg^22x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     22      
 |  tan  (x) dx
 |             
/              
0
∫01tan⁡22(x) dx\int\limits_{0}^{1} \tan^{22}{\left(x \right)}\, dx 
Integral(tan(x)^22, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                
 |                                    3           7            11            15            19           5           9            13            17            21    
 |    22                 sin(x)    sin (x)     sin (x)      sin  (x)      sin  (x)      sin  (x)     sin (x)     sin (x)      sin  (x)      sin  (x)      sin  (x) 
 | tan  (x) dx = C - x + ------ - --------- - --------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + -----------
 |                       cos(x)        3           7            11            15            19           5           9            13            17            21   
/                                 3*cos (x)   7*cos (x)   11*cos  (x)   15*cos  (x)   19*cos  (x)   5*cos (x)   9*cos (x)   13*cos  (x)   17*cos  (x)   21*cos  (x)
∫tan⁡22(x) dx=C−x+sin⁡21(x)21cos⁡21(x)−sin⁡19(x)19cos⁡19(x)+sin⁡17(x)17cos⁡17(x)−sin⁡15(x)15cos⁡15(x)+sin⁡13(x)13cos⁡13(x)−sin⁡11(x)11cos⁡11(x)+sin⁡9(x)9cos⁡9(x)−sin⁡7(x)7cos⁡7(x)+sin⁡5(x)5cos⁡5(x)−sin⁡3(x)3cos⁡3(x)+sin⁡(x)cos⁡(x)\int \tan^{22}{\left(x \right)}\, dx = C - x + \frac{\sin^{21}{\left(x \right)}}{21 \cos^{21}{\left(x \right)}} - \frac{\sin^{19}{\left(x \right)}}{19 \cos^{19}{\left(x \right)}} + \frac{\sin^{17}{\left(x \right)}}{17 \cos^{17}{\left(x \right)}} - \frac{\sin^{15}{\left(x \right)}}{15 \cos^{15}{\left(x \right)}} + \frac{\sin^{13}{\left(x \right)}}{13 \cos^{13}{\left(x \right)}} - \frac{\sin^{11}{\left(x \right)}}{11 \cos^{11}{\left(x \right)}} + \frac{\sin^{9}{\left(x \right)}}{9 \cos^{9}{\left(x \right)}} - \frac{\sin^{7}{\left(x \right)}}{7 \cos^{7}{\left(x \right)}} + \frac{\sin^{5}{\left(x \right)}}{5 \cos^{5}{\left(x \right)}} - \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-2000020000
Trazar el gráfico f(x)
Respuesta [src] 
                  3           7            11            15            19           5           9            13            17            21    
     sin(1)    sin (1)     sin (1)      sin  (1)      sin  (1)      sin  (1)     sin (1)     sin (1)      sin  (1)      sin  (1)      sin  (1) 
-1 + ------ - --------- - --------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + -----------
     cos(1)        3           7            11            15            19           5           9            13            17            21   
              3*cos (1)   7*cos (1)   11*cos  (1)   15*cos  (1)   19*cos  (1)   5*cos (1)   9*cos (1)   13*cos  (1)   17*cos  (1)   21*cos  (1)
−sin⁡19(1)19cos⁡19(1)−sin⁡15(1)15cos⁡15(1)−sin⁡11(1)11cos⁡11(1)−sin⁡7(1)7cos⁡7(1)−sin⁡3(1)3cos⁡3(1)−1+sin⁡(1)cos⁡(1)+sin⁡5(1)5cos⁡5(1)+sin⁡9(1)9cos⁡9(1)+sin⁡13(1)13cos⁡13(1)+sin⁡17(1)17cos⁡17(1)+sin⁡21(1)21cos⁡21(1)- \frac{\sin^{19}{\left(1 \right)}}{19 \cos^{19}{\left(1 \right)}} - \frac{\sin^{15}{\left(1 \right)}}{15 \cos^{15}{\left(1 \right)}} - \frac{\sin^{11}{\left(1 \right)}}{11 \cos^{11}{\left(1 \right)}} - \frac{\sin^{7}{\left(1 \right)}}{7 \cos^{7}{\left(1 \right)}} - \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} - 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}} + \frac{\sin^{9}{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}} + \frac{\sin^{13}{\left(1 \right)}}{13 \cos^{13}{\left(1 \right)}} + \frac{\sin^{17}{\left(1 \right)}}{17 \cos^{17}{\left(1 \right)}} + \frac{\sin^{21}{\left(1 \right)}}{21 \cos^{21}{\left(1 \right)}} 
=
= 
                  3           7            11            15            19           5           9            13            17            21    
     sin(1)    sin (1)     sin (1)      sin  (1)      sin  (1)      sin  (1)     sin (1)     sin (1)      sin  (1)      sin  (1)      sin  (1) 
-1 + ------ - --------- - --------- - ----------- - ----------- - ----------- + --------- + --------- + ----------- + ----------- + -----------
     cos(1)        3           7            11            15            19           5           9            13            17            21   
              3*cos (1)   7*cos (1)   11*cos  (1)   15*cos  (1)   19*cos  (1)   5*cos (1)   9*cos (1)   13*cos  (1)   17*cos  (1)   21*cos  (1)
−sin⁡19(1)19cos⁡19(1)−sin⁡15(1)15cos⁡15(1)−sin⁡11(1)11cos⁡11(1)−sin⁡7(1)7cos⁡7(1)−sin⁡3(1)3cos⁡3(1)−1+sin⁡(1)cos⁡(1)+sin⁡5(1)5cos⁡5(1)+sin⁡9(1)9cos⁡9(1)+sin⁡13(1)13cos⁡13(1)+sin⁡17(1)17cos⁡17(1)+sin⁡21(1)21cos⁡21(1)- \frac{\sin^{19}{\left(1 \right)}}{19 \cos^{19}{\left(1 \right)}} - \frac{\sin^{15}{\left(1 \right)}}{15 \cos^{15}{\left(1 \right)}} - \frac{\sin^{11}{\left(1 \right)}}{11 \cos^{11}{\left(1 \right)}} - \frac{\sin^{7}{\left(1 \right)}}{7 \cos^{7}{\left(1 \right)}} - \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} - 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}} + \frac{\sin^{9}{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}} + \frac{\sin^{13}{\left(1 \right)}}{13 \cos^{13}{\left(1 \right)}} + \frac{\sin^{17}{\left(1 \right)}}{17 \cos^{17}{\left(1 \right)}} + \frac{\sin^{21}{\left(1 \right)}}{21 \cos^{21}{\left(1 \right)}} 
-1 + sin(1)/cos(1) - sin(1)^3/(3*cos(1)^3) - sin(1)^7/(7*cos(1)^7) - sin(1)^11/(11*cos(1)^11) - sin(1)^15/(15*cos(1)^15) - sin(1)^19/(19*cos(1)^19) + sin(1)^5/(5*cos(1)^5) + sin(1)^9/(9*cos(1)^9) + sin(1)^13/(13*cos(1)^13) + sin(1)^17/(17*cos(1)^17) + sin(1)^21/(21*cos(1)^21)
Respuesta numérica [src] 
359.420953445668
359.420953445668

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

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