integral of (x^2-3)sin(2x)

Lösung

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

- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{2} x sin (2 x) + \frac{7}{4} cos (2 x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - x cos (2 x) d x = - \frac{1}{4} (2 x sin (2 x) + cos (2 x))

= - \frac{1}{2} cos (2 x) (x^{2} - 3) - (- \frac{1}{4} (2 x sin (2 x) + cos (2 x)))

Vereinfache

- \frac{1}{2} cos (2 x) (x^{2} - 3) - (- \frac{1}{4} (2 x sin (2 x) + cos (2 x))) : - \frac{1}{2} x^{2} cos (2 x) + \frac{1}{2} x sin (2 x) + \frac{7}{4} cos (2 x)

= - \frac{1}{2} x^{2} cos (2 x) + \frac{1}{2} x sin (2 x) + \frac{7}{4} cos (2 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} x^{2} cos (2 x) + \frac{1}{2} x sin (2 x) + \frac{7}{4} cos (2 x) + C

\frac{d}{d x} (e^{(- 5 x^{2} - 2 x^{2})})

\frac{d}{d x} (11 x)

\int 5 x - 7 d x

y^{^{'}} = k y \cdot (100 - y)

\int \frac{8 + 3 x}{1 + x ^{2}} d x