Integrais Imediatas

TABELA DE INTEGRAIS IMEDIATAS

Prof. MSc Henrique Starick

f1 ∫xα dx = xα + 1 + C para α ≠ - 1

α + 1

f2 ∫1 dx = ln|x| + C

x

f3 ∫ex dx = ex + C

f4 ∫ax dx = ax + C, a > 0

lna

f5 ∫cos x dx = sen x + C

f6 ∫sen x dx = -cos x + C

f7 ∫sec2 x dx = tg x + C

f8 ∫cosec2 x dx = -cotg x + C

f9 ∫sec x . tag x dx = sec x + C

f10 ∫cosec x . cotg x dx = -cosec x + C

f11 ∫ 1 dx = arc sen x + C

√ 1 – x2

f12 ∫ 1 dx = arc tag x + C

1 + x2

f13 ∫ 1 dx = arc sec x + C

x√x2 – 1

f14 ∫ cosh x dx = - senh x + C

f15 ∫ senh x dx = cosh x + C

f16 ∫ sech2 x dx = - tagh x + C

f17 ∫ cotgh2 x dx = cosech x + C

f18 ∫ sech x . tagh x dx = -sech x + C

f19 ∫cosech x . cotgh x dx = cosech x + C

f20 ∫ 1 dx = arc senh x + C = ln(x +√1+x2) + C

√ 1 + x2

f21 ∫ 1 dx = arc cosh x + C = ln( x + √x2 - 1 ) + C

√x2 - 1

f22 ∫ 1 dx = arc tagh x + C = 1 ln 1 + x + C

1 - x2 2 1 – x

f23 ∫ 1 dx = - arc cotgh x + C = 1 ln x + 1 + C

x2 – 1 2 x – 1

f24 ∫ 1 dx = - arc sech x + C = -ln 1 + √ 1 - x2 +C

x√1- x2 x

f25 ∫ 1 dx = - arc cosech x + C = -ln 1 +√ 1- x2 + C

|x|√1+ x2 x

F26 ∫tag x dx = - ln| cos x | + C

F27 ∫cotg x dx = ln |sen x| + C

F28 ∫sec x dx = ln | sec x + tag x | + C

F29 ∫cosec