tabla de integrales inmediatas - PROFESOR JANO es Víctor M. Vitoria

TABLA DE INTEGRALES INMEDIATAS
Caso general
Integral
Primitiva
Integral
Primitiva
∫ x ⋅ dx
x n+1
+C
n+1
ef(x) + C
∫ n ⋅ f ' ( x) ⋅ f
n−1
( x ) ⋅ dx
fn (x) + C, si n ≠ -1
∫ f ' ( x) ⋅ a
⋅ log a ⋅ dx
af(x) + C, si a > 0
f (x)
⌠ f ' ( x)
⋅ dx
⎮
⌡ f ( x)
Caso particular
Ln [f(x)] + C
n
∫ f ' ( x) ⋅ e
f ( x)
⋅ dx
⌠ 1 ⋅dx
⎮
⌡x
⌠ dx
⎮
⌡ (x − a )
⌠ dx
⎮
⌡ 1 − x2
Ln x + C
Ln (x-a) + C
⌠ f ' ( x ) ⋅ dx
⎮
⌡ 1 − f 2 ( x)
arc sen f(x) + C
⌠ − f ' ( x) ⋅ dx
⎮
⌡ 1 − f 2 ( x)
arc cos f(x) + C
⌠ − dx
⎮
⌡ 1− x2
arc cos x + C
arctg x + C
arc sen x + C
⌠ f ' ( x) ⋅ dx
⎮
2
⌡ 1 + f ( x)
⌠ − f ' ( x ) ⋅ dx
⎮
2
⌡ 1 + f ( x)
∫ f ' ( x) ⋅ cos f ( x) ⋅ dx
∫ − f ' ( x) ⋅ sen f ( x) ⋅ dx
arc tg f(x) + C
⌠ dx
⎮
⌡ 1+ x2
arc ctg f(x) + C
⌠ − dx
⎮
⌡ 1+ x2
arc ctg x + C
sen f(x) + C
cos f(x) + C
∫ cos x ⋅ dx
∫ − sen x ⋅ dx
sen x + C
cos x + C
⌠ f ' ( x ) ⋅ dx
⎮
2
⌡ cos f ( x )
tg f(x) + C
⌠ − f ' ( x ) ⋅ dx
⎮
2
⌡ sen f ( x )
cotg f(x) + C
∫ − f ' ( x) ⋅ tg f ( x) ⋅ dx
∫ f ' ( x) ⋅ cot g f ( x) ⋅ dx
© Prof. Víctor M. Vitoria
Ln [cos f(x)] + C
Ln [sen f(x)] + C
⌠ dx
⎮
⌡ cos x
⌠ − dx
⎮
2
⌡ sen x
∫ − tg x ⋅ dx
∫ cot g x ⋅ dx
tg x + C
cotg x + C
Ln [cos x] + C
Ln [sen x] + C
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