integral of (cos^2(x)-sin(x))/(cos(x))

Lösung

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

sin (x) + ln ∣ cos (x) ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{cos ^{2} ( x ) - sin ( x )}{cos ( x )} : cos (x) - \frac{sin ( x )}{cos ( x )}

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

\int cos (x) d x = sin (x)

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

= sin (x) - (- ln ∣ cos (x) ∣)

Vereinfache

= sin (x) + ln ∣ cos (x) ∣

Füge eine Konstante zur Lösung hinzu

= sin (x) + ln ∣ cos (x) ∣ + C

\int \frac{16}{x ^{2} + 4} d x

\int - y^{- 2} d y

\int 3 x (4 - x) d x

\int 10 e^{x} - x e^{x} + 1 d x

\int A e^{- k x} d x