cos(x) R cos(x)dx= sin(x) cos(x

Stammfunktion Funktion (=Definition) Ableitung R sin(x)dx =−cos(x) sin(t) :=p

1−cos²(t) sin⁰(x) = cos(x) R cos(x)dx= sin(x) cos(x) := arccos⁻¹(x) cos⁰(x) =−sin(x)

R tan(x)dx=−log(cos(x)) tan(t) = _cos(t)^sin(t) tan⁰(t) = _cos¹2(t) = 1 + tan²(t) R cot(x)dx= log(sin(x)) cot(t) = ^cos(t)_sin(t) cot⁰(x) =−_sin¹2(x) =−1−cot²(x) R log(x) =x·log(x)−x log(x) :=

x

R

1 dt

t log⁰(x) = _x¹

log_a(x) := ^log_log^x_a

R e^xdx=e^x e^x := log⁻¹(x) (e^x)⁰ = _log¹0(t) = ¹1 t

=t =e^x

Stammfunktion Funktion (=Definition) Ableitung

R arcsin(x)dx =x·arcsin(x) +√

1−x² arcsin(x) := sin⁻¹(x) arcsin⁰(x) = ^√1

1−x²

R arccos(x)dx=−x·arcsin(x)−√

1−x²+ ^π·x₂ arccos(x) :=

1

R

x

√1

1−t² dt = arccos⁰(x) = −^√_1−x¹ ₂

=x√

1−x²+ 2

1

R

x

√1−t²dt

R arctan(x)dx=x·arctan(x)− ^log(x₂²⁺¹⁾ arctan(t) = tan⁻¹(t) arctan⁰(x) = _1+x¹ 2

R arccot(x)dx=−x·arctan(x)− ^log(x₂²⁺¹⁾ + ^π·x₂ arccot(t) = cot⁻¹(t) arccot⁰(x) =−_1+x¹2

Stammfunktion Funktion (=Definition) Ableitung

R sinh(x)dx= ^e₂^x +^e−x₂ sinh(x) := ¹₂(e^x−e^−x) sinh⁰(x) = cosh(x) R cosh(x)dx= ^e₂^x − ^e−x₂ cosh(x) := ¹₂(e^x+e^−x) cosh⁰(x) = sinh(x) R tanh(x)dx= log[e^2x+ 1)−x tanh(x) := _cosh(x)^sinh(x) = ^e_e^xx^−e+e^−x−x tanh⁰(x) = _cosh¹2(x)

R coth(x)dx= log[e^2x−1)−x coth(x) := ^cosh(x)_sinh(x) = ^e_e^xx^+e−e^−x−x coth⁰(x) = _sinh¹2(x)

1