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Beliebt Rechnen >

integral of 1/(N(5-N))

Lösung

\int \frac{1}{N ( 5 - N )} d N

Lösung

\frac{1}{5} ln ∣ N ∣ - \frac{1}{5} ln ∣ N - 5 ∣ + C

Schritte zur Lösung

\int \frac{1}{N ( 5 - N )} d N

Ermittle den Partialbruch von

\frac{1}{N ( 5 - N )} : \frac{1}{5 N} - \frac{1}{5 ( N - 5 )}

= \int \frac{1}{5 N} - \frac{1}{5 ( N - 5 )} d N

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}{5 N} d N - \int \frac{1}{5 ( N - 5 )} d N

\int \frac{1}{5 N} d N = \frac{1}{5} ln ∣ N ∣

\int \frac{1}{5 ( N - 5 )} d N = \frac{1}{5} ln ∣ N - 5 ∣

= \frac{1}{5} ln ∣ N ∣ - \frac{1}{5} ln ∣ N - 5 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} ln ∣ N ∣ - \frac{1}{5} ln ∣ N - 5 ∣ + C

Graph

Beliebte Beispiele

integral of cos(x)(2+sin(x))^2

\int cos (x) (2 + sin (x))^{2} d x

integral of (5x-6)/(\sqrt[3]{x-1)}

\int \frac{5 x - 6}{3 x - 1} d x

integral of (3x)/(3x+1)

\int \frac{3 x}{3 x + 1} d x

integral of (2x+5)/(5x+9)

\int \frac{2 x + 5}{5 x + 9} d x

integral of ((ln(x)+1))/x

\int \frac{( ln ( x ) + 1 )}{x} d x