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Beliebt Rechnen >

integral of (x^2+3)sin(4x)

Lösung

\int (x^{2} + 3) sin (4 x) d x

Lösung

- \frac{1}{4} x^{2} cos (4 x) + \frac{1}{8} x sin (4 x) - \frac{23}{32} cos (4 x) + C

Schritte zur Lösung

\int (x^{2} + 3) sin (4 x) d x

Wende die partielle Integration an

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

\int - \frac{1}{2} x cos (4 x) d x = - \frac{1}{32} (4 x sin (4 x) + cos (4 x))

= - \frac{1}{4} cos (4 x) (x^{2} + 3) - (- \frac{1}{32} (4 x sin (4 x) + cos (4 x)))

Vereinfache

- \frac{1}{4} cos (4 x) (x^{2} + 3) - (- \frac{1}{32} (4 x sin (4 x) + cos (4 x))) : - \frac{1}{4} x^{2} cos (4 x) + \frac{1}{8} x sin (4 x) - \frac{23}{32} cos (4 x)

= - \frac{1}{4} x^{2} cos (4 x) + \frac{1}{8} x sin (4 x) - \frac{23}{32} cos (4 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} x^{2} cos (4 x) + \frac{1}{8} x sin (4 x) - \frac{23}{32} cos (4 x) + C

Graph

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