integral of ((50x+6))/((7x+1)(x-1))

Lösung

\int \frac{( 50 x + 6 )}{( 7 x + 1 ) ( x - 1 )} d x

\frac{1}{7} ln ∣ 7 x + 1 ∣ + 7 ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{50 x + 6}{( 7 x + 1 ) ( x - 1 )} d x

Ermittle den Partialbruch von

\frac{50 x + 6}{( 7 x + 1 ) ( x - 1 )} : \frac{1}{7 x + 1} + \frac{7}{x - 1}

= \int \frac{1}{7 x + 1} + \frac{7}{x - 1} 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}{7 x + 1} d x + \int \frac{7}{x - 1} d x

\int \frac{1}{7 x + 1} d x = \frac{1}{7} ln ∣ 7 x + 1 ∣

\int \frac{7}{x - 1} d x = 7 ln ∣ x - 1 ∣

= \frac{1}{7} ln ∣ 7 x + 1 ∣ + 7 ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{7} ln ∣ 7 x + 1 ∣ + 7 ln ∣ x - 1 ∣ + C

d er i v a t i v e g (u) = u + 1 (1 - 8 u^{2})^{7}

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

\int_{0}^{2} 2 x^{2} - x^{3} d x

\int \frac{x - 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x

x \to \infty lim (\frac{- 2}{x})