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Beliebt Rechnen >

integral of (sec(2θ)-csc(θ/2))

Lösung

\int (sec (2 θ) - csc (\frac{θ}{2})) d θ

Lösung

\frac{1}{2} ln ∣ tan (2 θ) + sec (2 θ) ∣ - 2 ln tan (\frac{θ}{4}) + C

Schritte zur Lösung

\int sec (2 θ) - csc (\frac{θ}{2}) d θ

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec (2 θ) d θ - \int csc (\frac{θ}{2}) d θ

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

\int csc (\frac{θ}{2}) d θ = 2 ln tan (\frac{θ}{4})

= \frac{1}{2} ln ∣ tan (2 θ) + sec (2 θ) ∣ - 2 ln tan (\frac{θ}{4})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln ∣ tan (2 θ) + sec (2 θ) ∣ - 2 ln tan (\frac{θ}{4}) + C

Graph

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