integral of sec(x)-tan(x)

Lösung

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

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

Schritte zur Lösung

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

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

\int tan (x) d x = - ln ∣ cos (x) ∣

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

in v erse l a pl a ce \frac{8.2}{4.2 x ^{2} + 4 x + 5}

in v erse l a pl a ce \frac{s ^{2}}{( s ^{2} - 1 ) ^{2}}

d er i v a t i v e \frac{10}{x ^{2}}

n = 0 \sum \infty \frac{6}{n ( n + 3 )}

f (t) = \frac{1}{t ^{2}}