Grundintegrale / 0dx = c / sinh xdx = cosh xdx / n + 1 + c, n ∈ R\{−1

Grundintegrale
ˆ
ˆ
0 dx = c
ˆ
xn dx =
ˆ
ˆ
sinh x dx = cosh x dx
ˆ
xn+1
+ c, n ∈ R\{−1}
n+1
cosh x dx = sinh x + c
ˆ
1
dx = ln |x| + c
x
x
tanh2 x dx = x − tanh x + c
ˆ
x
coth2 x dx = x − coth x + c
e dx = e + c
ˆ
ˆ
ax
+c
a dx =
ln a
1
2 dx = − coth x + c
ˆ sinh x
1
2 dx = tanh x + c
cosh
x
ˆ
1
1
2 dx = − x + a + c
(x + a)
ˆ
1
dx = ln |x + a| + c
x+a
ˆ
ln x dx = x · ln x − x + c
ˆ
ln x 1
2
x · ln x dx = x ·
−
+c
2
4
ˆ
1
1
sin2 ax dx = x −
sin ·2ax + c
2
4a
ˆ
1
1
sin ·2ax + c
cos2 ax dx = x +
2
4a
ˆ
1
1
dx = · ln |tan ax| + c
sin ax · cos ax
a
x
ˆ
sin x dx = − cos x + c
ˆ
cos x dx = sin x + c
ˆ
1
dx = tan x + c
cos2 x
ˆ
1
dx = − cot x + c
sin2 x
ˆ
tan2 x dx = tan x − x + c
ˆ
cot2 x dx = − cot x − x + c
ˆ
1
dx = arcsin x + c = − arccos x + c
2
1
−
x
ˆ
1
√
dx = arsinh x + c
x2 + 1
√
1