integral of (x^2+3x)cos(x)

Lösung

\int (x^{2} + 3 x) cos (x) d x

x^{2} sin (x) + 3 x sin (x) + 2 x cos (x) + 3 cos (x) - 2 sin (x) + C

Schritte zur Lösung

\int (x^{2} + 3 x) cos (x) d x

Wende die partielle Integration an

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

\int (2 x + 3) sin (x) d x = - cos (x) (2 x + 3) + 2 sin (x)

= (x^{2} + 3 x) sin (x) - (- cos (x) (2 x + 3) + 2 sin (x))

Vereinfache

(x^{2} + 3 x) sin (x) - (- cos (x) (2 x + 3) + 2 sin (x)) : x^{2} sin (x) + 3 x sin (x) + 2 x cos (x) + 3 cos (x) - 2 sin (x)

= x^{2} sin (x) + 3 x sin (x) + 2 x cos (x) + 3 cos (x) - 2 sin (x)

Füge eine Konstante zur Lösung hinzu

= x^{2} sin (x) + 3 x sin (x) + 2 x cos (x) + 3 cos (x) - 2 sin (x) + C

\frac{d}{d x} (x^{- 3} + \frac{1}{x ^{7}})

\int \frac{x + 1}{2 x - x ^{2}} d x

\frac{d}{d x} (\frac{- x ^{2}}{y ^{2}})

d er i v a t i v e f (x) = \frac{x ^{2}}{2} \cdot cos^{3} (\frac{1}{x})

n = 2 \sum \infty 3 (\frac{x}{4})^{n}