integral of sec^5(4x)

Lösung

\int sec^{5} (4 x) d x

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

Schritte zur Lösung

\int sec^{5} (4 x) d x

Wende U-Substitution an

= \int sec^{5} (u) \frac{1}{4} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int sec^{5} (u) d u

Wende integrale Reduktion an

= \frac{1}{4} (\frac{sec ^{4} ( u ) sin ( u )}{4} + \frac{3}{4} \cdot \int sec^{3} (u) d u)

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

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

Setze in

u = 4 x

ein

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (x^{x^{2} + y^{2}})

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)

n = 1 \sum \infty \frac{9}{10 0 ^{n}}

x \to 0 lim (g (x))

\frac{\partial}{\partial x} (2 x y)