integral of (tan(2x)-sec(2x))

Lösung

\int (tan (2 x) - sec (2 x)) d x

- \frac{1}{2} ln ∣ cos (2 x) ∣ - \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ + C

Schritte zur Lösung

\int tan (2 x) - sec (2 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 (2 x) d x - \int sec (2 x) d x

\int tan (2 x) d x = - \frac{1}{2} ln ∣ cos (2 x) ∣

\int sec (2 x) d x = \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣

= - \frac{1}{2} ln ∣ cos (2 x) ∣ - \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} ln ∣ cos (2 x) ∣ - \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ + C

\int \frac{x}{x ^{2} + 4 x + 5} d x

d er i v a t i v e \frac{9 - x ^{2}}{32 x}

d er i v a t i v e f (x) = 3 x^{3} (x^{2} - 2)

d er i v a t i v e f (x) = (3 x^{2} - 2) (5 x + 5)

\int \frac{1}{1 - cos ^{2} ( x )} d x