integral of x(cos(x)+1)

Lösung

\int x (cos (x) + 1) d x

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

Schritte zur Lösung

\int x (cos (x) + 1) d x

Wende die partielle Integration an

= x (sin (x) + x) - \int sin (x) + x d x

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

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