integral of x^2sin(θx)

Lösung

\int x^{2} sin (θ x) d x

- \frac{1}{θ} x^{2} cos (θ x) + \frac{2}{θ ^{3}} (θ x sin (θ x) + cos (θ x)) + C

Schritte zur Lösung

\int x^{2} sin (θ x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int_{0}^{5} π (x - 1)^{2} d x

2 y \frac{d y}{d x} + \frac{( 1 + y ^{2} )}{x} = 1

\int sin (π) x cos (π) x d x

x \to 5 lim (- x^{2} + x - 5)

\int \frac{3 x ^{2}}{x ^{2} + 1} d x