Sr Examen
Integral de tg^22x dx
Solución
Ha introducido
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1 / | | 22 | tan (x) dx | / 0
$$\int\limits_{0}^{1} \tan^{22}{\left(x \right)}\, dx$$
Integral(tan(x)^22, (x, 0, 1))
Respuesta (Indefinida)
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/ | 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)
$$\int \tan^{22}{\left(x \right)}\, dx = C - x + \frac{\sin^{21}{\left(x \right)}}{21 \cos^{21}{\left(x \right)}} - \frac{\sin^{19}{\left(x \right)}}{19 \cos^{19}{\left(x \right)}} + \frac{\sin^{17}{\left(x \right)}}{17 \cos^{17}{\left(x \right)}} - \frac{\sin^{15}{\left(x \right)}}{15 \cos^{15}{\left(x \right)}} + \frac{\sin^{13}{\left(x \right)}}{13 \cos^{13}{\left(x \right)}} - \frac{\sin^{11}{\left(x \right)}}{11 \cos^{11}{\left(x \right)}} + \frac{\sin^{9}{\left(x \right)}}{9 \cos^{9}{\left(x \right)}} - \frac{\sin^{7}{\left(x \right)}}{7 \cos^{7}{\left(x \right)}} + \frac{\sin^{5}{\left(x \right)}}{5 \cos^{5}{\left(x \right)}} - \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$$
Gráfica
Respuesta
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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)
$$- \frac{\sin^{19}{\left(1 \right)}}{19 \cos^{19}{\left(1 \right)}} - \frac{\sin^{15}{\left(1 \right)}}{15 \cos^{15}{\left(1 \right)}} - \frac{\sin^{11}{\left(1 \right)}}{11 \cos^{11}{\left(1 \right)}} - \frac{\sin^{7}{\left(1 \right)}}{7 \cos^{7}{\left(1 \right)}} - \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} - 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}} + \frac{\sin^{9}{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}} + \frac{\sin^{13}{\left(1 \right)}}{13 \cos^{13}{\left(1 \right)}} + \frac{\sin^{17}{\left(1 \right)}}{17 \cos^{17}{\left(1 \right)}} + \frac{\sin^{21}{\left(1 \right)}}{21 \cos^{21}{\left(1 \right)}}$$
=
=
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)
$$- \frac{\sin^{19}{\left(1 \right)}}{19 \cos^{19}{\left(1 \right)}} - \frac{\sin^{15}{\left(1 \right)}}{15 \cos^{15}{\left(1 \right)}} - \frac{\sin^{11}{\left(1 \right)}}{11 \cos^{11}{\left(1 \right)}} - \frac{\sin^{7}{\left(1 \right)}}{7 \cos^{7}{\left(1 \right)}} - \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} - 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}} + \frac{\sin^{9}{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}} + \frac{\sin^{13}{\left(1 \right)}}{13 \cos^{13}{\left(1 \right)}} + \frac{\sin^{17}{\left(1 \right)}}{17 \cos^{17}{\left(1 \right)}} + \frac{\sin^{21}{\left(1 \right)}}{21 \cos^{21}{\left(1 \right)}}$$
-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)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.