integral of (sech^2(x))/(tanh(x))

Lösung

\int \frac{sech ^{2} ( x )}{tanh ( x )} d x

ln ∣ sinh (x) ∣ - ln ∣ cosh (x) ∣ + C

Schritte zur Lösung

\int \frac{sech ^{2} ( x )}{tanh ( x )} d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Multipliziere aus

\frac{1 - tanh ^{2} ( x )}{tanh ( x )} : \frac{1}{tanh ( x )} - tanh (x)

= \int \frac{1}{tanh ( x )} - tanh (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}{tanh ( x )} d x - \int tanh (x) d x

\int \frac{1}{tanh ( x )} d x = ln ∣ sinh (x) ∣

\int tanh (x) d x = ln ∣ cosh (x) ∣

= ln ∣ sinh (x) ∣ - ln ∣ cosh (x) ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ sinh (x) ∣ - ln ∣ cosh (x) ∣ + C

\int_{0}^{1} (x^{2} + 5) e^{- x} d x

\int \frac{1000}{100 x} d x

\int_{0}^{3 - x} 3 - x - y d y

\frac{d}{d x} (x tan (\frac{1}{x}))

\int \frac{1}{( x + 3 ) ^{2} ( x - 5 )} d x