integral of tan(4x)-cot(x/4)

Lösung

\int tan (4 x) - cot (\frac{x}{4}) d x

- \frac{1}{4} ln ∣ cos (4 x) ∣ - 4 ln sin (\frac{x}{4}) + C

Schritte zur Lösung

\int tan (4 x) - cot (\frac{x}{4}) d x

Wende die Summenregel an:

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

= \int tan (4 x) d x - \int cot (\frac{x}{4}) d x

\int tan (4 x) d x = - \frac{1}{4} ln ∣ cos (4 x) ∣

\int cot (\frac{x}{4}) d x = 4 ln sin (\frac{x}{4})

= - \frac{1}{4} ln ∣ cos (4 x) ∣ - 4 ln sin (\frac{x}{4})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} ln ∣ cos (4 x) ∣ - 4 ln sin (\frac{x}{4}) + C

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