integral of sin(3x)-tan(2x)+5/(3x+2)

Lösung

\int sin (3 x) - tan (2 x) + \frac{5}{3 x + 2} d x

- \frac{1}{3} cos (3 x) + \frac{1}{2} ln ∣ cos (2 x) ∣ + \frac{5}{3} ln ∣ 3 x + 2 ∣ + C

Schritte zur Lösung

\int sin (3 x) - tan (2 x) + \frac{5}{3 x + 2} 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 sin (3 x) d x - \int tan (2 x) d x + \int \frac{5}{3 x + 2} d x

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

\int tan (2 x) d x = - \frac{1}{2} ln ∣ cos (2 x) ∣

\int \frac{5}{3 x + 2} d x = \frac{5}{3} ln ∣ 3 x + 2 ∣

= - \frac{1}{3} cos (3 x) - (- \frac{1}{2} ln ∣ cos (2 x) ∣) + \frac{5}{3} ln ∣ 3 x + 2 ∣

Vereinfache

= - \frac{1}{3} cos (3 x) + \frac{1}{2} ln ∣ cos (2 x) ∣ + \frac{5}{3} ln ∣ 3 x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} cos (3 x) + \frac{1}{2} ln ∣ cos (2 x) ∣ + \frac{5}{3} ln ∣ 3 x + 2 ∣ + C

\int 3 - 0.01 x + 0.00006 x^{2} d x

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