integral of 4sin(4x)sin(3x)cos(2x)

Lösung

\int 4 sin (4 x) sin (3 x) cos (2 x) d x

4 (- \frac{1}{10} sin (4 x) cos (5 x) - \frac{1}{2} sin (4 x) cos (x) + \frac{1}{5} sin (x) + \frac{1}{45} sin (9 x) + \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x)) + C

Schritte zur Lösung

\int 4 sin (4 x) sin (3 x) cos (2 x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int sin (4 x) sin (3 x) cos (2 x) d x

Wende die partielle Integration an

= 4 (\frac{1}{2} sin (4 x) (- \frac{1}{5} cos (5 x) - cos (x)) - \int 2 cos (4 x) (- \frac{1}{5} cos (5 x) - cos (x)) d x)

\int 2 cos (4 x) (- \frac{1}{5} cos (5 x) - cos (x)) d x = - \frac{1}{5} sin (x) - \frac{1}{45} sin (9 x) - \frac{1}{5} sin (5 x) - \frac{1}{3} sin (3 x)

= 4 (\frac{1}{2} sin (4 x) (- \frac{1}{5} cos (5 x) - cos (x)) - (- \frac{1}{5} sin (x) - \frac{1}{45} sin (9 x) - \frac{1}{5} sin (5 x) - \frac{1}{3} sin (3 x)))

Multipliziere aus

\frac{1}{2} sin (4 x) (- \frac{1}{5} cos (5 x) - cos (x)) - (- \frac{1}{5} sin (x) - \frac{1}{45} sin (9 x) - \frac{1}{5} sin (5 x) - \frac{1}{3} sin (3 x)) : - \frac{1}{10} sin (4 x) cos (5 x) - \frac{1}{2} sin (4 x) cos (x) + \frac{1}{5} sin (x) + \frac{1}{45} sin (9 x) + \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x)

= 4 (- \frac{1}{10} sin (4 x) cos (5 x) - \frac{1}{2} sin (4 x) cos (x) + \frac{1}{5} sin (x) + \frac{1}{45} sin (9 x) + \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x))

Füge eine Konstante zur Lösung hinzu

= 4 (- \frac{1}{10} sin (4 x) cos (5 x) - \frac{1}{2} sin (4 x) cos (x) + \frac{1}{5} sin (x) + \frac{1}{45} sin (9 x) + \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x)) + C

\frac{\partial}{\partial x} (e^{- 3 y} cos (3 x))

t \to - \infty lim (e^{t} + 1)

\frac{d}{d x} (0.01 (0.2 x^{2} + 4 x + 64)^{\frac{2}{3}})

\int_{0}^{10} x^{2} e^{- 0.08 x} d x

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