integral of cos((npix)/7)

Lösung

\int cos (\frac{nπ x}{7}) d x

\frac{7}{πn} sin (\frac{πn x}{7}) + C

Schritte zur Lösung

\int cos (\frac{nπ x}{7}) d x

Wende die partielle Integration an

= x cos (\frac{πn x}{7}) - \int - \frac{πn}{7} x sin (\frac{πn x}{7}) d x

\int - \frac{πn}{7} x sin (\frac{πn x}{7}) d x = x cos (\frac{πn x}{7}) - \frac{7}{πn} sin (\frac{πn x}{7})

= x cos (\frac{πn x}{7}) - (x cos (\frac{πn x}{7}) - \frac{7}{πn} sin (\frac{πn x}{7}))

Vereinfache

= \frac{7}{πn} sin (\frac{πn x}{7})

Füge eine Konstante zur Lösung hinzu

= \frac{7}{πn} sin (\frac{πn x}{7}) + C

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