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

Lösung

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

x - ln ∣ sin (x) ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{sin ( x ) - cos ( x )}{sin ( x )} : 1 - \frac{cos ( x )}{sin ( x )}

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

\int 1 d x = x

\int \frac{cos ( x )}{sin ( x )} d x = ln ∣ sin (x) ∣

= x - ln ∣ sin (x) ∣

Füge eine Konstante zur Lösung hinzu

= x - ln ∣ sin (x) ∣ + C

\int sin (3 y) ln (x)

\int \frac{9 x}{x ^{3} - 3 x + 2} d x

\int \frac{1}{x ^{4} x ^{2} - 36} d x

\int \frac{e x}{n} d x

\int x^{2} (x) d x