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integrales indefinidas Tarea 12 (soluci&Atilde;&sup3;n)

# integrales indefinidas Tarea 12...

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Calcule las integrales indefinidas dadas. 1. dx x x x 6 7 4 8 3 Solución: Tenemos que 3 2 1 ) 3 )( 2 )( 1 ( 4 8 6 7 4 8 3 x C x B x A x x x x x x x Luego ) 2 )( 1 ( ) 3 )( 1 ( ) 3 )( 2 ( 4 8 x x C x x B x x A x ) 2 3 ( ) 3 2 ( ) 6 ( 4 8 2 2 2 x x C x x B x x A x C B A x C B A x C B A x 2 3 6 ) 3 2 ( ) ( 4 8 2 de donde 0 C B A 8 3 2 C B A 4 2 3 6 C B A Resolviendo este sistema tenemos que A = -3 B = 4 C = -1 Así tenemos que 3 1 2 4 1 3 6 7 4 8 3 x x x x x x Luego dx x x x dx x x x ) 3 1 2 4 1 3 ( 6 7 4 8 3 dx x dx x dx x 3 1 2 1 4 1 1 3 K x x x ) 3 ln( ) 2 ln( 4 ) 1 ln( 3 Por tanto K x x x dx x x x ) 3 ln( ) 2 ln( 4 ) 1 ln( 3 6

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