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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{( x - 2 ) ^{4}}{4 x - x ^{2}} d x

\frac{d x}{d t} = 2 \frac{x}{t} - 0.194 t

\frac{\partial}{\partial x} (ln (x^{6} - y^{6}))

\frac{d}{d M} (\frac{2 π r ^{\frac{3}{2}}}{GM})

\frac{d}{d x} (x^{3} - \frac{4}{x})