integral of (tan(x)+sec(x))

Lösung

\int (tan (x) + sec (x)) d x

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

Schritte zur Lösung

\int tan (x) + sec (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 tan (x) d x + \int sec (x) d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial y} (\frac{e ^{x}}{1 + e ^{y}})

d er i v a t i v e f (x) = 3

\frac{d}{d θ} ((csc (θ) + cot (θ))^{- 1})

\frac{d y}{d x} + e^{x + y} = 0

\int \frac{x ^{2}}{( x ^{3} + 5 ) ^{2}} d x