...3 , avem EMBED Equation.3 , deci EMBED Equation.3 .Cazul 1. EMBED Equation.3 Sa punem EMBED Equation.3 unde EMBED Equation.3 .Atunci substitutia EMBED Equation.3 ne da EMBED Equation.3 ,deci EMBED Equation.3 unde EMBED Equation.3 este functie rationala deoarece EMBED Equation.3 .Cazul 2. EMBED Equation.3 Sa punem EMBED Equation.3 , unde EMBED Equation.3 .Atunci substitutia EMBED Equation.3 ,ne da EMBED Equation.3 ,deci EMBED Equation.3 unde EMBED Equation.3 este functie rationala deoarece EMBED Equation.3 .Cazul 3. EMBED Equation.3 Evident avem EMBED Equation.3 Sa punem EMBED Equation.3 , unde EMBED Equation.3 . Atunci substitutia EMBED Equation.3 , ne da EMBED Equation.3 ,deci EMBED Equation.3 unde EMBED Equation.3 este functie rationala deoarece EMBED Equation.3 .Concluzie.Prin urmare substitutile urmatoare EMBED Equation.3 , daca EMBED Equation.3 , unde EMBED Equation.3 EMBED Equation.3 , daca EMBED Equation.3 , unde EMBED Equation.3 EMBED Equation.3 , daca EMBED Equation.3 , unde EMBED Equation.3 , reduc calculul primitivei EMBED Equation.3 la calculul primitivei dintr-o functie rationala .Observatie.Cebisev a aratat ca daca EMBED Equation.3 , EMBED Equation.3 si EMBED Equation.3 ,atunci primitiva data nu se poate reduce la primitiva dintr-o functie rationala . Calculul primitivei nu poate fi facut atunci prin mijloace elementare .Exemplul 1.Sa se calculeze primitiva EMBED Equation.3 .Avem EMBED Equation.3 , deci suntem in cazul 1.Cum EMBED Equation.3 facem substitutia EMBED Equation.3 , deci EMBED Equation.3 si deci EMBED Equation.3 Exemplul 2.Sa se calculeze primitiva EMBED Equation.3 Avem EMBED Equation.3 si deci suntem in cazul 2.Facem substitutia EMBED Equation.3 .Atunci EMBED Equation.3 , de unde obtinem EMBED Equation.3 Exemplul 3.Sa se calculeze primitiva EMBED Equation.3 Avem EMBED Equation.3 , EMBED Equation.3 si EMBED Equation.3 ,deci EMBED Equation.3 si deci suntem in cazul 3. Facem substitutia EMBED Equation.3 . Atunci EMBED Equation.3 , de unde obtinem EMBED Equation.3 Exemplul 4.Sa se calculeze primitiva EMBED Equation.3 Avem functia F EMBED Equation.3 unde EMBED Equation.3 EMBED Equation.3 Facem substitutia EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 si obtinem EMBED Equation.3 Exemplul 5.Sa se calculeze primitiva EMBED Equation.3 Avem EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 Facem substitutia EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 si obtinem EMBED Equation.3 Exemplul 6.Se se calculeze primitiva EMBED Equation.3 Avem EMBED Equation.3 , deci suntem in cazul 1.Consideram EMBED Equation.3 , unde EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 si obtinem EMBED Equation.3 mnaiaiaiaiaiaiyaiaidVaiaiaj6hàEHOJaQJaUajhàOJaQJaU
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