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Beliebt Rechnen >

integral of 5/x-x/5

Lösung

\int \frac{5}{x} - \frac{x}{5} d x

Lösung

5 ln ∣ x ∣ - \frac{x ^{2}}{10} + C

Schritte zur Lösung

\int \frac{5}{x} - \frac{x}{5} 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 \frac{5}{x} d x - \int \frac{x}{5} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{x}{5} d x = \frac{x ^{2}}{10}

= 5 ln ∣ x ∣ - \frac{x ^{2}}{10}

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x ∣ - \frac{x ^{2}}{10} + C

Graph

Beliebte Beispiele

integral of 1/((1+y))

\int \frac{1}{( 1 + y )} d y

integral of 1/(1-cos^4(x))

\int \frac{1}{1 - cos ^{4} ( x )} d x

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

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

integral of (x+sin(x))^3(1+cos(x))

\int (x + sin (x))^{3} (1 + cos (x)) d x

integral of (3x+1)^{18}

\int (3 x + 1)^{18} d x