integral of (x^2+6x)cos(x)

Lösung

\int (x^{2} + 6 x) cos (x) d x

x^{2} sin (x) + 6 x sin (x) + 2 x cos (x) + 6 cos (x) - 2 sin (x) + C

Schritte zur Lösung

\int (x^{2} + 6 x) cos (x) d x

Wende die partielle Integration an

= (x^{2} + 6 x) sin (x) - \int (2 x + 6) sin (x) d x

\int (2 x + 6) sin (x) d x = - cos (x) (2 x + 6) + 2 sin (x)

= (x^{2} + 6 x) sin (x) - (- cos (x) (2 x + 6) + 2 sin (x))

Vereinfache

(x^{2} + 6 x) sin (x) - (- cos (x) (2 x + 6) + 2 sin (x)) : x^{2} sin (x) + 6 x sin (x) + 2 x cos (x) + 6 cos (x) - 2 sin (x)

= x^{2} sin (x) + 6 x sin (x) + 2 x cos (x) + 6 cos (x) - 2 sin (x)

Füge eine Konstante zur Lösung hinzu

= x^{2} sin (x) + 6 x sin (x) + 2 x cos (x) + 6 cos (x) - 2 sin (x) + C

\frac{d}{d x} (e^{a x^{6}})

d er i v a t i v e f (x) = (x)^{3} \cdot e^{(3 x)}

2 y^{2} = \frac{d y}{d x}

\int_{1}^{e} \frac{( x ^{2} - 1 )}{x} d x

\frac{d}{d t} (e^{- 2 t})