integral (sin^2(x))/(cos(x))

Lösung

integral

\frac{sin ^{2} ( x )}{cos ( x )}

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

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Multipliziere aus

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

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

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

\int cos (x) d x = sin (x)

= ln ∣ tan (x) + sec (x) ∣ - sin (x)

Füge eine Konstante zur Lösung hinzu

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

in t e g r a l \frac{( e ^{- x} ) ^{2}}{2}

in t e g r a l \frac{1}{( x ^{2} + y ^{2} )}

in t e g r a l a^{2} - x^{2}

in t e g r a l x^{2} a^{2} - x^{2}

in t e g r a l \frac{sin ( x )}{2}