integral of (x^5-5x+4)/(x^2)

Lösung

\int \frac{x ^{5} - 5 x + 4}{x ^{2}} d x

\frac{x ^{4}}{4} - 5 ln ∣ x ∣ - \frac{4}{x} + C

Schritte zur Lösung

\int \frac{x ^{5} - 5 x + 4}{x ^{2}} d x

Multipliziere aus

\frac{x ^{5} - 5 x + 4}{x ^{2}} : x^{3} - \frac{5}{x} + \frac{4}{x ^{2}}

= \int x^{3} - \frac{5}{x} + \frac{4}{x ^{2}} 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^{3} d x - \int \frac{5}{x} d x + \int \frac{4}{x ^{2}} d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

= \frac{x ^{4}}{4} - 5 ln ∣ x ∣ - \frac{4}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - 5 ln ∣ x ∣ - \frac{4}{x} + C

\int \frac{4 x}{5 x ^{2} + 2} d x

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

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

\int \frac{1}{( x x ^{2} + 1 )} d x

\int \frac{- 2 x}{( 2 x + 4 ) - 4 x + 8} d x