integral of sec^{13}(x)

Lösung

\int sec^{13} (x) d x

\frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} (\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))) + C

Schritte zur Lösung

\int sec^{13} (x) d x

Wende integrale Reduktion an

= \frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} \cdot \int sec^{11} (x) d x

\int sec^{11} (x) d x = \frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))

= \frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} (\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣)))))

Füge eine Konstante zur Lösung hinzu

= \frac{sec ^{12} ( x ) sin ( x )}{12} + \frac{11}{12} (\frac{1}{10} sec^{10} (x) sin (x) + \frac{3}{1280} (48 sec^{8} (x) sin (x) + 7 (8 sec^{6} (x) sin (x) + 5 (2 sec^{4} (x) sin (x) + 3 (sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣))))) + C