integral of sec^5(x)

Lösung

\int sec^{5} (x) d x

\frac{sec ^{4} ( x ) sin ( x )}{4} + \frac{3}{4} (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

Schritte zur Lösung

\int sec^{5} (x) d x

Wende integrale Reduktion an

= \frac{sec ^{4} ( x ) sin ( x )}{4} + \frac{3}{4} \cdot \int sec^{3} (x) d x

\int sec^{3} (x) d x = \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= \frac{sec ^{4} ( x ) sin ( x )}{4} + \frac{3}{4} (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Füge eine Konstante zur Lösung hinzu

= \frac{sec ^{4} ( x ) sin ( x )}{4} + \frac{3}{4} (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

t an g e n t f (x) = x x, at x = 0

\int \frac{1}{x ^{2} + 8 x + 32} d x

x \to 7 - lim (\frac{x}{x ^{2} - 49})

a re a x + 1, 9 - x^{2}, - 1, 2

y^{^{'}} = (x + y)^{2} - 1, y (1) = 6