integral of (x^2+7x)cos(x)

Lösung

\int (x^{2} + 7 x) cos (x) d x

x^{2} sin (x) + 7 x sin (x) + 2 x cos (x) + 7 cos (x) - 2 sin (x) + C

Schritte zur Lösung

\int (x^{2} + 7 x) cos (x) d x

Wende die partielle Integration an

= (x^{2} + 7 x) sin (x) - \int (2 x + 7) sin (x) d x

\int (2 x + 7) sin (x) d x = - cos (x) (2 x + 7) + 2 sin (x)

= (x^{2} + 7 x) sin (x) - (- cos (x) (2 x + 7) + 2 sin (x))

Vereinfache

(x^{2} + 7 x) sin (x) - (- cos (x) (2 x + 7) + 2 sin (x)) : x^{2} sin (x) + 7 x sin (x) + 2 x cos (x) + 7 cos (x) - 2 sin (x)

= x^{2} sin (x) + 7 x sin (x) + 2 x cos (x) + 7 cos (x) - 2 sin (x)

Füge eine Konstante zur Lösung hinzu

= x^{2} sin (x) + 7 x sin (x) + 2 x cos (x) + 7 cos (x) - 2 sin (x) + C

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

\int \frac{x + 23}{x ^{2} + 20 x + 104} d x

\int_{0}^{2 π} x e^{- i x} d x

\int 3 x^{2} ln (x) d x

x \to 0 lim (- 2 g (x))