integral of (2x+4)/(x^2-10x+16)

Lösung

\int \frac{2 x + 4}{x ^{2} - 10 x + 16} d x

- \frac{4}{3} ln ∣ x - 2 ∣ + \frac{10}{3} ln ∣ x - 8 ∣ + C

Schritte zur Lösung

\int \frac{2 x + 4}{x ^{2} - 10 x + 16} d x

Ermittle den Partialbruch von

\frac{2 x + 4}{x ^{2} - 10 x + 16} : - \frac{4}{3 ( x - 2 )} + \frac{10}{3 ( x - 8 )}

= \int - \frac{4}{3 ( x - 2 )} + \frac{10}{3 ( x - 8 )} 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{4}{3 ( x - 2 )} d x + \int \frac{10}{3 ( x - 8 )} d x

\int \frac{4}{3 ( x - 2 )} d x = \frac{4}{3} ln ∣ x - 2 ∣

\int \frac{10}{3 ( x - 8 )} d x = \frac{10}{3} ln ∣ x - 8 ∣

= - \frac{4}{3} ln ∣ x - 2 ∣ + \frac{10}{3} ln ∣ x - 8 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{4}{3} ln ∣ x - 2 ∣ + \frac{10}{3} ln ∣ x - 8 ∣ + C

\int [\frac{2}{7} (3^{x})] d x

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

\int e^{- (x^{2})^{2}} d (x^{2})^{2}

\int 4 x^{3} e^{- x} d x

\int \frac{1}{13 x - 7} d x