integral of xcos((nx)/2)

Lösung

\int x cos (\frac{n x}{2}) d x

\frac{2}{n} x sin (\frac{n x}{2}) + \frac{4}{n ^{2}} cos (\frac{n x}{2}) + C

Schritte zur Lösung

\int x cos (\frac{n x}{2}) d x

Wende die partielle Integration an

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

\int \frac{2}{n} sin (\frac{n x}{2}) d x = - \frac{4}{n ^{2}} cos (\frac{n x}{2})

= \frac{2}{n} x sin (\frac{n x}{2}) - (- \frac{4}{n ^{2}} cos (\frac{n x}{2}))

Vereinfache

= \frac{2}{n} x sin (\frac{n x}{2}) + \frac{4}{n ^{2}} cos (\frac{n x}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{2}{n} x sin (\frac{n x}{2}) + \frac{4}{n ^{2}} cos (\frac{n x}{2}) + C

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