integral of (sec(4x)-csc((2x)/3))

Lösung

\int (sec (4 x) - csc (\frac{2 x}{3})) d x

\frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{3}{2} ln tan (\frac{x}{3}) + C

Schritte zur Lösung

\int sec (4 x) - csc (\frac{2 x}{3}) 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 sec (4 x) d x - \int csc (\frac{2 x}{3}) d x

\int sec (4 x) d x = \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣

\int csc (\frac{2 x}{3}) d x = \frac{3}{2} ln tan (\frac{x}{3})

= \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{3}{2} ln tan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ - \frac{3}{2} ln tan (\frac{x}{3}) + C

\int \frac{9 x ^{8} + 6}{( x ^{9} + 6 x ) ^{2}} d x

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