integral of 1/(1-2x)-cos(x/3)

Lösung

\int \frac{1}{1 - 2 x} - cos (\frac{x}{3}) d x

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

Schritte zur Lösung

\int \frac{1}{1 - 2 x} - cos (\frac{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 \frac{1}{1 - 2 x} d x - \int cos (\frac{x}{3}) d x

\int \frac{1}{1 - 2 x} d x = - \frac{1}{2} ln ∣ 1 - 2 x ∣

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

= - \frac{1}{2} ln ∣ 1 - 2 x ∣ - 3 sin (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

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

ma c l a u r in \frac{1}{3 x ^{2} + 8}

y^{^{''}} - y^{^{'}} - 2 y = - 4 t + 6 t^{2}

\int x e^{6} d x

a re a 3 x, \frac{1}{x}, [1, 8]

d er i v a t i v e f (x) = - 2 x + 3