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Beliebt Rechnen >

integral of cos(ax)cos(bx)

Lösung

\int cos (a x) cos (b x) d x

Lösung

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

Schritte zur Lösung

\int cos (a x) cos (b x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{cos ( a x + b x ) + cos ( a x - b x )}{2} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int cos (a x + b x) + cos (a x - b 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

= \frac{1}{2} (\int cos (a x + b x) d x + \int cos (a x - b x) d x)

\int cos (a x + b x) d x = \frac{1}{a + b} sin (a x + b x)

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

limit as x approaches 2 of (x^2-a)/(x-2)

x \to 2 lim (\frac{x ^{2} - a}{x - 2})

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d er i v a t i v e 2 x^{3} - 3

(\partial)/(\partial y)(2y-2)

\frac{\partial}{\partial y} (2 y - 2)

derivative of e^xcos(9x)

\frac{d}{d x} (e^{x} cos (9 x))

inverselaplace 1/(s^2-4s+5)

in v erse l a pl a ce \frac{1}{s ^{2} - 4 s + 5}