integral of (x^2+1)/((x-7)(x-6))

Lösung

\int \frac{x ^{2} + 1}{( x - 7 ) ( x - 6 )} d x

x + 50 ln ∣ x - 7 ∣ - 37 ln ∣ x - 6 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} + 1}{( x - 7 ) ( x - 6 )} d x

Ermittle den Partialbruch von

\frac{x ^{2} + 1}{( x - 7 ) ( x - 6 )} : 1 + \frac{50}{x - 7} - \frac{37}{x - 6}

= \int 1 + \frac{50}{x - 7} - \frac{37}{x - 6} 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 1 d x + \int \frac{50}{x - 7} d x - \int \frac{37}{x - 6} d x

\int 1 d x = x

\int \frac{50}{x - 7} d x = 50 ln ∣ x - 7 ∣

\int \frac{37}{x - 6} d x = 37 ln ∣ x - 6 ∣

= x + 50 ln ∣ x - 7 ∣ - 37 ln ∣ x - 6 ∣

Füge eine Konstante zur Lösung hinzu

= x + 50 ln ∣ x - 7 ∣ - 37 ln ∣ x - 6 ∣ + C

\int \frac{e ^{2 t}}{1 + e ^{4 t}} d t

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

y \to \infty lim (\frac{2 y ^{2} - 3 y + 5}{y ^{2} - 5 y + 2})

x \to 2 lim (x^{3} + 3 x^{2})

\frac{d v}{d t} = k \cdot (275 - v), v (0) = 0