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

Lösung

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

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int (7 - 2 x)^{11} d x

\int - \frac{cos ( n x )}{n} d x

\int - 3 cos (t) d t

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 cos (2 t) e^{t}

d er i v a t i v e y = \frac{2 x}{3 - cot ( x )}