integral of sec^3(θ)

Lösung

\int sec^{3} (θ) d θ

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

Schritte zur Lösung

\int sec^{3} (θ) d θ

Wende integrale Reduktion an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

t a y l or ∣ sin (x) ∣

x \to 0 - lim (\frac{cos ( x )}{x})

d er i v a t i v e 5 x + 2

\frac{d}{d x} (5^{3 x^{3}})

\int \frac{1}{- x ^{2} - 14 x - 48} d x