Tabla de integrales inmediatas

I.E.S. "Fernando de Mena"
Departamento de Matemáticas
Pedro Castro Ortega
Tabla de integrales inmediatas
Funciones simples
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Funciones compuestas
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dx =
−−
1 dx = x + C
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−−
k dx = kx + C
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xn+1
+ C ; n 6= −1
x dx =
n+1
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1
dx = ln x + C
x
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ex dx = ex +C
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n
Z
Z
Z
Z
1
· ax + C
a dx =
ln a
x
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Z
ln x dx = x ln x − x + C
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f 0 (x)f (x)n dx =
1
loga x dx =
(x ln x − x) + C
ln a
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sen x dx = − cos x + C
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f 0 (x) ef (x) dx = ef (x) +C
f 0 (x)af (x) dx =
f 0 (x) loga f (x)dx =
Z
1
· af (x) + C
ln a
cos x dx = sen x + C
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1
(f (x) ln f (x) − f (x)) + C
ln a
f 0 (x) sen f (x) dx = − cos f (x) + C
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tg x dx = − ln(cos x) + C
f 0 (x)
dx = ln f (x) + C
f (x)
f 0 (x) ln f (x) dx = f (x) ln f (x) − f (x) + C
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Z
f (x)n+1
+ C ; n 6= −1
n+1
f 0 (x) cos f (x) dx = sen f (x) + C
f 0 (x) tg f (x) dx = − ln(cos f (x)) + C
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Z
Z
1
f 0 (x)
2
0
2
dx
=
(1
+
tg
x)
dx
=
tg
x
+
C
dx
=
f
(x)
1
+
tg
f
(x)
dx = tg f (x) + C
cos2 x
cos2 f (x)
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Z
Z
Z
1
f 0 (x)
2
dx = (1 + ctg x) dx = − ctg x + C
dx = f 0 (x) 1 + ctg2 f (x) dx = − ctg f (x) + C
2
2
sen x
sen f (x)
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Z
1
f 0 (x)
√
p
dx = arc sen x + C
dx = arc sen f (x) + C
1 − x2
1 − f (x)2
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Z
−1
−f 0 (x)
√
p
dx = arc cos x + C
dx = arc cos f (x) + C
1 − x2
1 − f (x)2
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Z
1
f 0 (x)
dx
=
arc
tg
x
+
C
dx = arc tg f (x) + C
1 + x2
1 + f (x)2
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