integral of 8sin^2(x)-2sin(x)-1

Lösung

\int 8 sin^{2} (x) - 2 sin (x) - 1 d x

3 x - 2 sin (2 x) + 2 cos (x) + C

Schritte zur Lösung

\int 8 sin^{2} (x) - 2 sin (x) - 1 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 8 sin^{2} (x) d x - \int 2 sin (x) d x - \int 1 d x

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

\int 2 sin (x) d x = - 2 cos (x)

\int 1 d x = x

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

Vereinfache

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

= 3 x - 2 sin (2 x) + 2 cos (x)

Füge eine Konstante zur Lösung hinzu

= 3 x - 2 sin (2 x) + 2 cos (x) + C

t an g e n t f (x) = \frac{3}{x}, at x = 1

d er i v a t i v e f (x) = \frac{3 x ^{2}}{x ^{3} - 8}

d er i v a t i v e 4 x^{10 x^{3}}

f (x) = ln (3^{2 - x^{2}})

\int \frac{x + 4}{x + 2} d x