Calculo 2
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GUIDG.COM – PG. 1 27/9/2010 – CDI-1: TABELA DE INTEGRAIS IMEDIATAS (u, v, w) são variáveis ; (a, b, c) constantes ; e ≈ 2,7182 , ln u = loge u ; sin = seno ; cos = cosseno ; tan = tangente ; cot = cotangente ; sec = secante ; csc = cossecante ; arc = arco ; h = hiperbólico ; arg = argumento ; s = substituiçõesIN Integral Imediata IN Integral Imediata
(1) Z du F dv =Z du F Z dv
uffff ffff fff fff (5) Z u a du = +c , a ≠@1 a +1
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`
a
(2) Z b dw = b Z dw
(3) Z du = u + c (7) Z e u du = e u + c
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a+1
aff fff fff ff (6) Z a u du = +c u ln a
(8) Z udv = vu @Z vdu
L M duf ff ff ff f (4) Z =Z u@ 1 du = lnLuM+ c
u
Z sin u du = @ cos u + c Z cos u du = sin u + c Z sec 2 u du = tan u + c Z csc 2 u du = @ cot u + c Z sec u A tan u du = sec u + c Z csc u A cot u du = @ csc u + c
Z sinh u du = cosh u + c Z cosh u du = sinh u + c Z sech u du = tanh u + c
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10
16
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Z csch u du = @ coth u + c
2
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Z sech u A tanh u du = @ sech u + c Z csch u A coth u du = @ csch u + c
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♦Z
fffffff ffffff ffffff fdu fff ff wwww = arc sin u wwww www www www www www ww q1 @ u 2 qa 2 @ u 2
+c
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uf ffdufff fff ffff fff fff fff fff ff f f www w = wwww wwww wwww w www wwww ww w ♦ Z fwwfwwf arc sin f+ c a
Z
\ 1 L1 + u M du ff \ f f ffff f ffff fffM fff f fffff arg tanh u + c , se | u | < 1 ou ffff ffff ff L M+ c = lnL 26 Z =Z Z 2 L1 @ u M arg coth u + c , se | u | > 1 1 @ u2
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X
L
M
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1 + u2
du ff ffff ffff ffff ff
= arc tan u + c f g d e
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uf fdufff 1f fffff ff ff ff f f f f Z fffff= f arc tan f + c 2 2 u +a a a
L M
L fffffff ffffff ffffff fdu fff ff q 2 L www www www www www www www 28 Z wwww = arg cosh u + c = lnLu + u @ 1 2 qu
L M ff ff ff ff ff f fdufff ffff f Z fwfwff arg sinh u + c = lnLu + q u 2 + 1 M + c wwww = ww w ww w ww w ww w ww w ww w L M q1 + u 2 L
wwwwM www www www www www w ww ww
@1
L
29
fff ff ff