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193
Integrály vybraných elementárních funkcí
1. 0 dx = C
2. k dx = kx + C , k ∈ R, konstanta
3. xn
dx =
xn+1
n + 1
+ C , n ∈ R, n = −1
4. 1
x
dx = ln |x| + C , x = 0
5. ax
dx =
ax
ln a
+ C , a > 0, a = 1 specielně ex
dx = ex
+ C
6. cos x dx = sin x + C
7. sin x dx = − cos x + C
8.
1
cos2 x
dx = tg x + C , x = (2k + 1)π
2
, k ∈ Z
9.
1
sin2
x
dx = −cotg x + C , x = kπ, k ∈ Z
10.
1
√
1 − x2
dx = arcsin x + C , (resp. − arccos x + C) , x ∈ (−1, 1)
11.
1
1 + x2
dx = arctg x + C , (resp. −arccotg x + C)
12.
1
√
x2 + a
dx = [ln(x +
√
a + x2)] + C , a = 0
13.
f′
(x)
f(x)
dx = ln |f(x)| + C , f(x) = 0 .
Tab. 10.1