integral of (x^3-8)/(x^2+8)

Lösung

\int \frac{x ^{3} - 8}{x ^{2} + 8} d x

\frac{1}{2} (x^{2} + 8 - 8 ln x^{2} + 8) - 22 arctan (\frac{x}{2 2}) + C

Schritte zur Lösung

\int \frac{x ^{3} - 8}{x ^{2} + 8} d x

Multipliziere aus

\frac{x ^{3} - 8}{x ^{2} + 8} : \frac{x ^{3}}{x ^{2} + 8} - \frac{8}{x ^{2} + 8}

Wende die Summenregel an:

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

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

\int \frac{x ^{3}}{x ^{2} + 8} d x = \frac{1}{2} (x^{2} + 8 - 8 ln x^{2} + 8)

\int \frac{8}{x ^{2} + 8} d x = 22 arctan (\frac{x}{2 2})

= \frac{1}{2} (x^{2} + 8 - 8 ln x^{2} + 8) - 22 arctan (\frac{x}{2 2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (x^{2} + 8 - 8 ln x^{2} + 8) - 22 arctan (\frac{x}{2 2}) + C

\int cos^{2} (ω x + φ) d x

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

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

\int (1 + tan (3 t))^{3} sec^{2} (3 t) d t

\int cos^{7} (6 x) sin (6 x) d x