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Beliebt Rechnen >

integral of 2cos(2x+pi/2)

Lösung

\int 2 cos (2 x + \frac{π}{2}) d x

Lösung

2 x cos (2 x + \frac{π}{2}) + 2 x sin (2 x) + cos (2 x) + C

Schritte zur Lösung

\int 2 cos (2 x + \frac{π}{2}) d x

Entferne die Konstante:

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

= 2 \cdot \int cos (2 x + \frac{π}{2}) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

= 2 x cos (2 x + \frac{π}{2}) + 2 x sin (2 x) + cos (2 x)

Füge eine Konstante zur Lösung hinzu

= 2 x cos (2 x + \frac{π}{2}) + 2 x sin (2 x) + cos (2 x) + C

Graph

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