integral of sec^2(x)sec(x)

Lösung

\int sec^{2} (x) sec (x) d x

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

Schritte zur Lösung

\int sec^{2} (x) sec (x) d x

Vereinfache

sec^{2} (x) sec (x) : sec^{3} (x)

= \int sec^{3} (x) d x

Wende integrale Reduktion an

= \frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} \cdot \int sec (x) d x

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

= \frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

Vereinfache

\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ : \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

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

Füge eine Konstante zur Lösung hinzu

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