integral of 2sec^3(x)

Lösung

\int 2 sec^{3} (x) d x

sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣ + C

Schritte zur Lösung

\int 2 sec^{3} (x) d x

Entferne die Konstante:

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

= 2 \cdot \int sec^{3} (x) d x

Wende integrale Reduktion an

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

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

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

Vereinfache

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

= sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣

Füge eine Konstante zur Lösung hinzu

= sec (x) tan (x) + ln ∣ tan (x) + sec (x) ∣ + C

\frac{\partial}{\partial x} (\frac{10 x}{36 + x ^{2} + y ^{2}})

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

\frac{\partial}{\partial x} (e^{x y} + 2 x - 5 y)

y^{^{''}} + 8 y^{^{'}} + 7 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

\frac{d ^{2}}{d x ^{2}} (x^{4} - 6 x^{3})