integral of xcos^2(x/2)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{x ^{2}}{2 + 2 x ^{2}} d x

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