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Beliebt Rechnen >

integral of 5sec^3(x)

Lösung

\int 5 sec^{3} (x) d x

Lösung

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

Schritte zur Lösung

\int 5 sec^{3} (x) d x

Entferne die Konstante:

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

= 5 \cdot \int sec^{3} (x) d x

Wende integrale Reduktion an

= 5 (\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) ∣

= 5 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Vereinfache

5 (\frac{sec ^{2} ( x ) sin ( x )}{2} + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) : 5 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

= 5 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

Graph

Beliebte Beispiele

derivative of e^{2x}sin(2x)

\frac{d}{d x} (e^{2 x} sin (2 x))

derivative of ((sqrt(x))/(x+1))

\frac{d}{d x} (\frac{( x )}{x + 1})

derivative of (x^2+1e^{-x})

\frac{d}{d x} ((x^{2} + 1) e^{- x})

derivative y=(7x-3)/(5x+4)+x^3

d er i v a t i v e y = \frac{7 x - 3}{5 x + 4} + x^{3}

integral of 8e^{2x}

\int 8 e^{2 x} d x