integral of x^2(-cos(x))'

Lösung

\int x^{2} (- cos (x))^{'} d x

\frac{1}{3} x^{3} (- cos (x))' - \frac{1}{3} x^{3} sin (x) - x^{2} cos (x) + 2 x sin (x) + 2 cos (x) + C

Schritte zur Lösung

\int x^{2} (- cos (x))^{'} d x

Wende die partielle Integration an

= \frac{1}{3} x^{3} (- cos (x))^{^{'}} - \int \frac{1}{3} x^{3} cos (x) d x

\int \frac{1}{3} x^{3} cos (x) d x = \frac{1}{3} x^{3} sin (x) + x^{2} cos (x) - 2 x sin (x) - 2 cos (x)

= \frac{1}{3} x^{3} (- cos (x))^{^{'}} - (\frac{1}{3} x^{3} sin (x) + x^{2} cos (x) - 2 x sin (x) - 2 cos (x))

Vereinfache

= \frac{1}{3} x^{3} (- cos (x))^{^{'}} - \frac{1}{3} x^{3} sin (x) - x^{2} cos (x) + 2 x sin (x) + 2 cos (x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} (- cos (x))^{^{'}} - \frac{1}{3} x^{3} sin (x) - x^{2} cos (x) + 2 x sin (x) + 2 cos (x) + C

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