integral of (ln(cos(x)))/(cos^2(x))

Lösung

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

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

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int ln (cos (x)) sec^{2} (x) d x

Wende die partielle Integration an

= ln (cos (x)) tan (x) - \int - tan^{2} (x) d x

\int - tan^{2} (x) d x = x - tan (x)

= ln (cos (x)) tan (x) - (x - tan (x))

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

t a y l or \frac{1}{sin ( x )}

t a y l or f (x) = e^{- 2 x}

\frac{1}{x ^{2}} \frac{d y}{d x} = 25 + 14 y

t an g e n t f (x) = x x, at x = 16

a re a sec^{2} (x), 8 cos (x)