integral of x^2sin(8x)

Lösung

\int x^{2} sin (8 x) d x

- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)) + C

Schritte zur Lösung

\int x^{2} sin (8 x) d x

Wende die partielle Integration an

= - \frac{1}{8} x^{2} cos (8 x) - \int - \frac{1}{4} x cos (8 x) d x

\int - \frac{1}{4} x cos (8 x) d x = - \frac{1}{256} (8 x sin (8 x) + cos (8 x))

= - \frac{1}{8} x^{2} cos (8 x) - (- \frac{1}{256} (8 x sin (8 x) + cos (8 x)))

Vereinfache

= - \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)) + C

d er i v a t i v e arcsin (3 x) + arccos (3 x)

\frac{d}{d x} (- \frac{2 x ( - x ^{2} + 27 )}{( x ^{2} + 9 ) ^{3}})

x \to 0 + lim (x^{10 x})

\frac{\partial}{\partial x} (x^{5} + y^{5} - 5 x^{3} y^{3})

x \to 1 lim (\frac{x ^{2} - 1}{x + 2})