integral of (40-2/(sec(x)))

Lösung

\int (40 - \frac{2}{sec ( x )}) d x

40 x - 2 sin (x) + C

Schritte zur Lösung

\int 40 - \frac{2}{sec ( x )} d x

Verwende die grundlegende trigonometrische Identität:

\frac{1}{sec ( x )} = cos (x)

= \int 40 - 2 cos (x) 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 40 d x - \int 2 cos (x) d x

\int 40 d x = 40 x

\int 2 cos (x) d x = 2 sin (x)

= 40 x - 2 sin (x)

Füge eine Konstante zur Lösung hinzu

= 40 x - 2 sin (x) + C

x \to 9 lim (7 x - 4)

d er i v a t i v e f (x) = (x - 3) (4 x + 2)

d er i v a t i v e f (x) = 2 sin^{2} (3 x) + 2 cos^{2} (3 x)

\int_{- 2}^{2} x + 2 d x

d er i v a t i v e f (x) = (\frac{x - 4}{x + 4})^{4}