integral of (x^2+5x)cos(x)

Lösung

\int (x^{2} + 5 x) cos (x) d x

x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x) + C

Schritte zur Lösung

\int (x^{2} + 5 x) cos (x) d x

Wende die partielle Integration an

= (x^{2} + 5 x) sin (x) - \int (2 x + 5) sin (x) d x

\int (2 x + 5) sin (x) d x = - cos (x) (2 x + 5) + 2 sin (x)

= (x^{2} + 5 x) sin (x) - (- cos (x) (2 x + 5) + 2 sin (x))

Vereinfache

(x^{2} + 5 x) sin (x) - (- cos (x) (2 x + 5) + 2 sin (x)) : x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x)

= x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x)

Füge eine Konstante zur Lösung hinzu

= x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x) + C

\frac{d y}{d x} = 0.5 y

x \to 0 + lim (\frac{∣ 2 x ∣}{x})

n \to \infty lim (A r g (- 1 + \frac{i}{n}))

in v erse l a pl a ce \frac{0.5}{s \cdot ( s ^{2} + s + 1 )}

\frac{d x}{d t} - (tan (t)) x = sin (t), x (0) = 1