integral of ((cos(x)+sin(x)))/(sin(2x))

Lösung

\int \frac{( cos ( x ) + sin ( x ) )}{sin ( 2 x )} d x

\frac{1}{2} ln tan (\frac{x}{2}) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

Schritte zur Lösung

\int \frac{cos ( x ) + sin ( x )}{sin ( 2 x )} d x

Multipliziere aus

\frac{cos ( x ) + sin ( x )}{sin ( 2 x )} : \frac{cos ( x )}{sin ( 2 x )} + \frac{sin ( x )}{sin ( 2 x )}

= \int \frac{cos ( x )}{sin ( 2 x )} + \frac{sin ( x )}{sin ( 2 x )} 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{cos ( x )}{sin ( 2 x )} d x + \int \frac{sin ( x )}{sin ( 2 x )} d x

\int \frac{cos ( x )}{sin ( 2 x )} d x = \frac{1}{2} ln tan (\frac{x}{2})

\int \frac{sin ( x )}{sin ( 2 x )} d x = \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= \frac{1}{2} ln tan (\frac{x}{2}) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln tan (\frac{x}{2}) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + C

\frac{d}{d x} (C x e^{x})

\int_{0}^{1} 6

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

\frac{\partial}{\partial x} (\frac{3 x - 2 y}{x ^{2} + 3 y})

\int \frac{cos ( x )}{sin ^{2} ( x ) - 36} d x