integral of (x^2+4)^2

Lösung

\int (x^{2} + 4)^{2} d x

\frac{x ^{5}}{5} + \frac{8 x ^{3}}{3} + 16 x + C

Schritte zur Lösung

\int (x^{2} + 4)^{2} d x

Multipliziere aus

(x^{2} + 4)^{2} : x^{4} + 8 x^{2} + 16

= \int x^{4} + 8 x^{2} + 16 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 x^{4} d x + \int 8 x^{2} d x + \int 16 d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 16 d x = 16 x

= \frac{x ^{5}}{5} + \frac{8 x ^{3}}{3} + 16 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + \frac{8 x ^{3}}{3} + 16 x + C

x \to \infty lim (- 5 x^{3})

\int x^{3} - 3 x d x

\frac{d}{d x} (100 e^{x})

y^{^{''}} + y = tan (x)

t an g e n t f (x) = x^{2} + x, at x = 3