integral cos^2(x)-1

Lösung

integral

cos^{2} (x) - 1

- \frac{1}{2} x + \frac{1}{4} sin (2 x) + C

Schritte zur Lösung

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

\int cos^{2} (x) d x = \frac{1}{2} (x + \frac{1}{2} sin (2 x))

\int 1 d x = x

= \frac{1}{2} (x + \frac{1}{2} sin (2 x)) - x

Vereinfache

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) - x : - \frac{1}{2} x + \frac{1}{4} sin (2 x)

= - \frac{1}{2} x + \frac{1}{4} sin (2 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} x + \frac{1}{4} sin (2 x) + C

in t e g r a l \frac{x}{x + 3}

in t e g r a l e^{\frac{1}{2}} x^{2}

in t e g r a l y = ∣ x - 1 ∣

in t e g r a l 2 x^{2} + 5

in t e g r a l e^{x} + 1