integral of 1/(x(100-x))

Lösung

\int \frac{1}{x ( 100 - x )} d x

\frac{1}{100} ln ∣ x ∣ - \frac{1}{100} ln ∣ x - 100 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ( 100 - x )} d x

Ermittle den Partialbruch von

\frac{1}{x ( 100 - x )} : \frac{1}{100 x} - \frac{1}{100 ( x - 100 )}

= \int \frac{1}{100 x} - \frac{1}{100 ( x - 100 )} 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}{100 x} d x - \int \frac{1}{100 ( x - 100 )} d x

\int \frac{1}{100 x} d x = \frac{1}{100} ln ∣ x ∣

\int \frac{1}{100 ( x - 100 )} d x = \frac{1}{100} ln ∣ x - 100 ∣

= \frac{1}{100} ln ∣ x ∣ - \frac{1}{100} ln ∣ x - 100 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{100} ln ∣ x ∣ - \frac{1}{100} ln ∣ x - 100 ∣ + C

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

d er i v a t i v e f (x) = \frac{1}{x ^{17}}

in v erse l a pl a ce \frac{1}{( s - 1 ) ( s ^{2} + 9 )}

a re a 2 x^{2} - 8 x - 55, - x^{2} - 2 x + 50, - 5, 7

\frac{\partial}{\partial y} (e^{x z} y^{3} - ln (x))