integral of sec^5(t)

Lösung

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

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

Schritte zur Lösung

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

Wende integrale Reduktion an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial ^{2}}{\partial x ^{2}} (x^{2} - e^{y^{2}})

d er i v a t i v e ln ∣ sec (θ) + tan (θ) ∣

\int_{0}^{1} \frac{x ^{4} + 2}{x} d x

d er i v a t i v e \frac{s - 1}{s + 1}

\frac{\partial}{\partial x} (e^{y} e^{x})