integral of sin(2x)x^2

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int_{0}^{4} 2 π x (x) d x

\int (6 x)^{3} d x

n = 1 \sum \infty 4^{n} \cdot x^{n}

n = 1 \sum \infty \frac{1}{3 n + 1}

\frac{d}{d x} (csc (x^{2}))