integral of cos(x)(8+8sin^2(x))

Lösung

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

8 sin (x) + \frac{8 sin ^{3} ( x )}{3} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int 8 + 8 u^{2} d u

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 d u + \int 8 u^{2} d u

\int 8 d u = 8 u

\int 8 u^{2} d u = \frac{8 u ^{3}}{3}

= 8 u + \frac{8 u ^{3}}{3}

Setze in

u = sin (x)

ein

= 8 sin (x) + \frac{8 sin ^{3} ( x )}{3}

Füge eine Konstante zur Lösung hinzu

= 8 sin (x) + \frac{8 sin ^{3} ( x )}{3} + C

t an g e n t y = 3 x^{2} + 2, at x = 1

\int x tan (x^{2}) d x

\frac{d y}{d x} = 2 x y + 3 y - 4 x - 6

\frac{x d y}{d x} = 6 y

x \to 7 lim (x^{2} - 49)