Odgovor:
Odgovor na to vprašanje =
Pojasnilo:
Za to vzemite tanx = t
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Kaj je integral int ((x ^ 2-1) / sqrt (2x-1)) dx?
Int (x ^ 2-1) / sqrt (2x-1) dx = 1/20 (2x-1) ^ (5/2) +1/6 (2x-1) ^ (3/2) -3 / 4sqrt (2x-1) + C Naš velik problem v tem integralu je koren, zato se ga želimo znebiti. To lahko naredimo z uvedbo zamenjave u = sqrt (2x-1). Derivat je torej (du) / dx = 1 / sqrt (2x-1) Torej delimo s (in zapomnimo, delimo z recipročnostjo je isto kot pomnožimo s samo imenovalcem), da se integriramo glede na u: int t x ^ 2-1) / sqrt (2x-1) dx = int (x ^ 2-1) / preklic (sqrt (2x-1)) preklic (sqrt (2x-1)) du = int t ^ 2-1 Vse kar moramo storiti je, da izrazimo x ^ 2 v smislu u (ker ne morete integrirati x glede na u): u = sqrt (2x-1) u ^ 2 = 2x- 1
Kaj je (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3-) sqrt (5))?
2/7 vzamemo, A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5) -sqrt3) / (2sqrt3-sqrt5) = (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) ) (2sqrt3 + sqrt5) ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15-5 + 2 * 3-sqrt15)) / ((2sqrt3)) ^ 2- (sqrt5) ^ 2) = (prekliči (2sqrt15) -5 + 2 * 3zaključi (-sqrt15) - prekliči (2sqrt15) -5 + 2 * 3 + prekliči (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Upoštevajte, da če je v imenovalcu (sqrt3 + sqrt (3 + sqrt5)) in (sqrt3 + sqrt (3-sqrt5)), bo odgovor spremenjen.
Kako poenostavite (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / ( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?
Ogromno oblikovanje matematike ...> barva (modra) (((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / ((a-1) sqrt (a + 1) - (a + 1) sqrt (a-1))) = barva (rdeča) (((1 / sqrt (a- 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = barva ( modro) ((((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a -1)))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = barva (rdeča) ((1 / sqr