алгебраик иррационалликларни интеграллаш

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1662925497.doc dx x x x r ) ,..., , ( ò g b a g b a ,..., , ) ,..., , ( ò g b a x x x r g b a ,..., , dx d cx b ax d cx b ax d cx b ax x r ] ) ( ,..., ) ( , ) ( , [ ò + + + + + + g b a g b a ,..., , n z d cx b ax = + + d cx b ax + + b ax + n z b ax = + g b a ,..., , = - = - = = = = = - = - ò ò ò ò ) 1 ( 6 6 6 3 7 4 3 5 2 6 5 6 3 2 2 1 3 1 3 2 3 z z dz z …

þ ï ï þ ï ï ý ü = - - = - + = - = + + d c b a d b a z c b a z bd a z c b a z = + - + + - - = + - ò ò ò 1 2 1 1 1 1 1 2 z dz z dz z dz dx x x x = + - - + = + - - - + = c arctgz z z c arctgz z z 2 1 1 ln 2 1 ln 1 ln = + + - - + - - + + - = + + - - - + - + + - = c x x arctg x x x x c x x arctg x x x x 1 1 2 1 1 1 1 ln 1 1 2 1 1 …

3 1 1 5 ) 1 5 ( 10 1 3 1 1 5 3 1 2 2 2 2 2 c x x c x x + + - = + + - = 2 2 3 15 15 1 3 5 5 c bx ax + + 2 ò + + dx c bx ax x r ) , ( 2 a ac b a b x a c bx ax 4 4 ) 2 ( 2 2 2 - - + = + + dz dx z a b x = = + , 2 ò ò + = + + dz z n m z r dx c bx ax x r ) , ( ) , ( 2 2 2 1 2 2 n a = 2 2 4 4 m a ac b = - - tgt n m z = ò t)dt t; …

) 1 ( 3 3 3 ) 3 3 ( 2 2 2 c t tg tgt cost dt t cos dt t cos dt cost cost t sin t cos dt t sin cost + + + = + = + = + = ò ò ò ò p = + + - + + = + = + + + = + = 1 3 1 8 2 1 1 ) 2 4 ( , 1 , 1 3 2 x x x x cost t sin t tg x 8 - 2x x t sin x cost 2 p 3 8 2 1 2 - + + + = x x x . 3 8 2 ) 1 ( ln 3 8 2 8 2 ) 4 ( 2 2 2 c x x x x x x x dx x + - + + + + …

t x th = 2 2 1 2 t t shx - = 2 2 1 1 t t chx - + = 2 1 2 t dt dx + = c x sh x x xd ch dx dx x ch xdx ch + + = + = + = ò ò ò ò 2 4 1 2 1 ) 2 ( 2 2 1 2 1 2 1 ) 1 2 ( 2 1 2 . 3 ) ( ) ( ) ( ) 1 ( 3 2 2 2 3 c chx x ch chx d chx xd ch chx d x ch xshxdx sh xdx sh + - = - = - = = ò ò ò ò ò = + - = - = = ò ò ò c x x sh dx x ch xdx sh xdx xch sh 8 1 4 4 1 …

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1662925497.doc dx x x x r ) ,..., , ( ò g b a g b a ,..., , ) ,..., , ( ò g b a x x x r g b a ,..., , dx d cx b ax d cx b ax d cx b ax x r ] ) ( ,..., ) ( , ) ( , [ ò + + + + + + g b a g b a ,..., , n z d cx b ax = + + d cx b ax + + b ax + n z b ax = + g b a ,..., , = - = - = = = = = - = - ò ò …

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