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Beliebt Rechnen >

integral of 1/(x(200-x))

Lösung

\int \frac{1}{x ( 200 - x )} d x

Lösung

\frac{1}{200} ln ∣ x ∣ - \frac{1}{200} ln ∣ x - 200 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ( 200 - x )} d x

Ermittle den Partialbruch von

\frac{1}{x ( 200 - x )} : \frac{1}{200 x} - \frac{1}{200 ( x - 200 )}

= \int \frac{1}{200 x} - \frac{1}{200 ( x - 200 )} 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{1}{200 x} d x - \int \frac{1}{200 ( x - 200 )} d x

\int \frac{1}{200 x} d x = \frac{1}{200} ln ∣ x ∣

\int \frac{1}{200 ( x - 200 )} d x = \frac{1}{200} ln ∣ x - 200 ∣

= \frac{1}{200} ln ∣ x ∣ - \frac{1}{200} ln ∣ x - 200 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{200} ln ∣ x ∣ - \frac{1}{200} ln ∣ x - 200 ∣ + C

Graph

Beliebte Beispiele

integral of ((1-2x)/3)^3

\int (\frac{1 - 2 x}{3})^{3} d x

integral of (5x^2-12)/(x^2-6x+13)

\int \frac{5 x ^{2} - 12}{x ^{2} - 6 x + 13} d x

integral of-(2sqrt(z))/3

\int - \frac{2 z}{3} d z

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

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

integral of (3x^2-x+1/(2x^3))

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