Sec 17

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…

¨ ¨¨ ¨ .. ¨ ¨...... α ¨ . β c b b a cos(α) = b a cos(β) = c a tangente: tg(α) = c b tg(β) = b c cotangente: ctg(α) = b c ctg(β) = c b secante: ... sen(β) = sec(α) = a b sec(β) = a c cossecante: a c a cosseno: ....¨ ¨¨......... sen(α) = csc(α) = a c csc(β) = a b Figura 7.2: As razões trigonométricas. Na Figura 7.3(a) traçamos a diagonal de um quadrado de lado a e então

eu du = eu + c. sen u du = − cos u + c. cos u du = sen u + c. tg u du = ln |sec u| + c. cotg u du = ln |sen u| + c. sec u du = ln |sec u + tg u| + c. cosec u du = ln |cosec u − cotg u| + c. sec u tg u du = sec u + c. cosec u cotg u du = −cosec u + c. sec2 u du = tg u + c. cosec2 u du = −cotg u + c. du 1 = a arc tg u + c. a u2 +a2 du u2 −a2 1 = 2a ln √ du u2 +a2 √ du u2 −a2 √ du = arc sen u + c, a a2 −u2 1 √ du = a arc sec u a u u2 −a2 Sejam u e v fun¸˜es deriv´veis de x e n conco a…