integral of ((x^4+2))/(x^3+9x)

Lösung

\int \frac{( x ^{4} + 2 )}{x ^{3} + 9 x} d x

\frac{x ^{2}}{2} - \frac{83}{18} ln x^{2} + 9 + \frac{2}{9} ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x ^{4} + 2}{x ^{3} + 9 x} d x

Lange Division

\frac{x ^{4} + 2}{x ^{3} + 9 x} : x + \frac{- 9 x ^{2} + 2}{x ^{3} + 9 x}

= \int x + \frac{- 9 x ^{2} + 2}{x ^{3} + 9 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 x d x + \int \frac{- 9 x ^{2} + 2}{x ^{3} + 9 x} d x

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

\int \frac{- 9 x ^{2} + 2}{x ^{3} + 9 x} d x = - \frac{83}{18} ln x^{2} + 9 + \frac{2}{9} ln ∣ x ∣

= \frac{x ^{2}}{2} - \frac{83}{18} ln x^{2} + 9 + \frac{2}{9} ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - \frac{83}{18} ln x^{2} + 9 + \frac{2}{9} ln ∣ x ∣ + C

\int (θ^{8} + sec^{2} (θ)) d θ

t a y l or sin (x), \frac{2 π}{3}

\int (4 x - sin (x)) d x

\int_{5}^{1} (- 4 x + 1) d x

x \to 3 - lim (2)