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Beliebt Rechnen >

integral of 1/(p(1-0.05p))

Lösung

\int \frac{1}{p ( 1 - 0.05 p )} d p

Lösung

ln ∣ p ∣ - ln ∣ 0.05 p - 1 ∣ + C

Schritte zur Lösung

\int \frac{1}{p ( 1 - 0.05 p )} d p

Ermittle den Partialbruch von

\frac{1}{p ( 1 - 0.05 p )} : \frac{1}{p} - \frac{0.05}{0.05 p - 1}

= \int \frac{1}{p} - \frac{0.05}{0.05 p - 1} d p

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}{p} d p - \int \frac{0.05}{0.05 p - 1} d p

\int \frac{1}{p} d p = ln ∣ p ∣

\int \frac{0.05}{0.05 p - 1} d p = ln ∣ 0.05 p - 1 ∣

= ln ∣ p ∣ - ln ∣ 0.05 p - 1 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ p ∣ - ln ∣ 0.05 p - 1 ∣ + C

Graph

Beliebte Beispiele

integral of 12sec^2(6x)tan(6x)

\int 12 sec^{2} (6 x) tan (6 x) d x

integral of 1/((x+1)(x+5))

\int \frac{1}{( x + 1 ) ( x + 5 )} d x

derivative y=cos(a^9+x^9)

d er i v a t i v e y = cos (a^{9} + x^{9})

tangent y=6x^2-3x,\at 1,5

t an g e n t y = 6 x^{2} - 3 x, at 1, 5

slopeintercept (8.1)(4.1)

s l o p e in t erce pt (8.1) (4.1)