integral of 5cos(3x)-4sin(5x)

Lösung

\int 5 cos (3 x) - 4 sin (5 x) d x

\frac{5}{3} sin (3 x) + \frac{4}{5} cos (5 x) + C

Schritte zur Lösung

\int 5 cos (3 x) - 4 sin (5 x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 cos (3 x) d x - \int 4 sin (5 x) d x

\int 5 cos (3 x) d x = \frac{5}{3} sin (3 x)

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

= \frac{5}{3} sin (3 x) - (- \frac{4}{5} cos (5 x))

Vereinfache

= \frac{5}{3} sin (3 x) + \frac{4}{5} cos (5 x)

Füge eine Konstante zur Lösung hinzu

= \frac{5}{3} sin (3 x) + \frac{4}{5} cos (5 x) + C

d er i v a t i v e lo g_{5} (x)

a re a \frac{1}{3} x^{\frac{1}{2}} - x^{\frac{3}{2}}, x = 0, x = \frac{1}{3}

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

x \to 4 - lim (\frac{7}{x - 4})

\frac{\partial}{\partial x} (\frac{6}{x ^{4}})