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

Lösung

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

- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{2} x sin (2 x) - \frac{11}{4} cos (2 x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= - \frac{1}{2} cos (2 x) (x^{2} + 6) - \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} + 6) - (- \frac{1}{4} (2 x sin (2 x) + cos (2 x)))

Vereinfache

- \frac{1}{2} cos (2 x) (x^{2} + 6) - (- \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{11}{4} cos (2 x)

= - \frac{1}{2} x^{2} cos (2 x) + \frac{1}{2} x sin (2 x) - \frac{11}{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{11}{4} cos (2 x) + C

ma c l a u r in ln (e + x)

\int_{0}^{0.5} x (4 - 8 x) d x

\int x cos (n x) d x

t a y l or 1 - 2 x^{2}

x \to 4 lim (x - 5)