integral of (cos(x))/(1-cos(x))

Lösung

\int \frac{cos ( x )}{1 - cos ( x )} d x

- cot (\frac{x}{2}) - x + C

Schritte zur Lösung

\int \frac{cos ( x )}{1 - cos ( x )} d x

\frac{cos ( x )}{1 - cos ( x )} = \frac{1}{1 - cos ( x )} - 1

= \int \frac{1}{1 - cos ( x )} - 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{1 - cos ( x )} d x - \int 1 d x

\int \frac{1}{1 - cos ( x )} d x = - cot (\frac{x}{2})

\int 1 d x = x

= - cot (\frac{x}{2}) - x

Füge eine Konstante zur Lösung hinzu

= - cot (\frac{x}{2}) - x + C

n = 9 \sum \infty e^{7 - 4 n}

\frac{\partial}{\partial x} (e^{7 x + 7 y})

x \to - 5 lim (\frac{x + 5}{5 - ∣ x ∣})

d er i v a t i v e cos (arcsin (x))

t an g e n t f (x) = 2 sin^{2} (π x), at x = \frac{3}{4}