Integral

isTABELA DE INTEGRAIS IMEDIATAS 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 ∫ f12 ∫ f13 ∫ 1 dx = arc sen x + C √ 1 – x2 1 1 + x2 dx = arc tag x + C

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 x dx = - ln | cosec x + cotag x | + C F30 ∫sec x . tag x dx = sec x + C F31 ∫cosec x . cotag x dx = - cosec x + C

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 2 √1+x f21 ∫ ∫

1 dx = arc cosh x + C = ln( x + √x 2 - 1 ) + C √x - 1
2

f22 f23

1 dx = arc tagh x + C = 1 ln 1 + x + C 1 - x2 2 1–x ∫ 1 dx = - arc cotgh x + C = 1 ln x + 1 + C x2 – 1 2 x–1 1 dx = - arc sech x + C = -ln 1 + √ 1 - x2 +C 2 x√1- x x

f24 ∫

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