Integración de funciones trigonométricas con multiples ángulos ejemplo 9


Esto es lo que usted escribira:

cos[2x]^2 sin[3x]

∫cos(2 x)^2 sin(3 x) dx
<br />        UsandoIntegraciónporpartes<br />& ... nbsp;du = -2/3 sin(4 x) dx, v = -cos(3 x) . <br />        
= -1/3 cos(3 x) cos^2(2 x) - ∫4/3 cos(2 x) cos(3 x) sin(2 x) dx
<br />        Factorizandoconstantess . <br />        
= -1/3 cos(3 x) cos^2(2 x) - 4/3∫cos(2 x) cos(3 x) sin(2 x) dx
<br />        Uselaformulaparaángulosmultiples< ... ;    dondem = 2yn = 3 . <br />        
= -1/3 cos(3 x) cos^2(2 x) - 4/3∫ (1/2 cos(2 x) sin(5 x) - 1/2 cos(2 x) sin(x)) dx
<br />        Integrandolasumatérmino-por-términoyfactorizandolasconstantes . <br />        
= -1/3 cos(3 x) cos^2(2 x) + 2/3∫cos(2 x) sin(x) dx - 2/3∫cos(2 x) sin(5 x) dx
<br />        Paracos(2 x) sin(5 x), uselaformulapara& ... ;    dondem = 5yn = 2 . <br />        
= -1/3 cos(3 x) cos^2(2 x) + 2/3∫cos(2 x) sin(x) dx - 2/3∫ (1/2 sin(3 x) + 1/2 sin(7 x)) dx
<br />        Integrando1/2 sin(3 x) + 1/2 sin(7 x) t& ... -términoyfactorizandolasconstantes . <br />        
= -1/3 cos(3 x) cos^2(2 x) + 2/3∫cos(2 x) sin(x) dx - 1/3∫sin(3 x) dx - 1/3∫sin(7 x) dx
<br />        Paracos(2 x) sin(x), uselaformulapara&aa ... ;    dondem = 1yn = 2 . <br />        
= -1/3 cos(3 x) cos^2(2 x) + 2/3∫ (1/2 sin(3 x) - sin(x)/2) dx - 1/3∫sin(3 x) dx - 1/3∫sin(7 x) dx
<br />        Integrando1/2 sin(3 x) - sin(x)/2t&eacut ... -términoyfactorizandolasconstantes . <br />        
= -1/3 cos(3 x) cos^2(2 x) - 1/3∫sin(x) dx - 1/3∫sin(7 x) dx
<br />        Paraelintegrantesin(7 x), <br /> &n ... sp;     ds = 7dx . <br />        
= -1/3 cos(3 x) cos^2(2 x) - 1/21∫sin(s) ds - 1/3∫sin(x) dx
<br />        Laintegraldesin(x) es -cos(x) . <br />        
= -1/3 cos(3 x) cos^2(2 x) + cos(x)/3 - 1/21∫sin(s) ds
<br />        Laintegraldesin(s) es -cos(s) . <br />        
= -1/3 cos(3 x) cos^2(2 x) + cos(s)/21 + cos(x)/3 + <span class=
<br />        Resustituyendos = 7 x . <br />        
= -1/3 cos(3 x) cos^2(2 x) + cos(x)/3 + 1/21 cos(7 x) + <span class=

Created by Mathematica  (March 9, 2003)