integral of (1+cos(x)+sin(x))/(cos(x))

Lösung

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

ln ∣ tan (x) + sec (x) ∣ + x - ln ∣ cos (x) ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int 1 d x = x

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

= ln ∣ tan (x) + sec (x) ∣ + x - ln ∣ cos (x) ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ tan (x) + sec (x) ∣ + x - ln ∣ cos (x) ∣ + C

\int \frac{4 x}{x + 1} d x

\int 10 x e^{2 x} d x

\int \frac{cos ( x )}{sin ^{2} ( x ) + 4} d x

in t e g r a l x^{2} + 1

\int \frac{6}{3 x} d x