integral of x^2sin(2Ax)

Lösung

\int x^{2} sin (2 A x) d x

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

Schritte zur Lösung

\int x^{2} sin (2 A x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d y}{d x} = 4 y e^{x + 10}

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t an g e n t f (x) = 4 x - 1, at x = 16