integral of x/(8x-7)

Lösung

\int \frac{x}{8 x - 7} d x

\frac{1}{64} (8 x - 7 + 7 ln ∣ 8 x - 7 ∣) + C

Schritte zur Lösung

\int \frac{x}{8 x - 7} d x

Wende U-Substitution an

= \int \frac{u + 7}{64 u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{64} \cdot \int \frac{u + 7}{u} d u

Multipliziere aus

\frac{u + 7}{u} : 1 + \frac{7}{u}

= \frac{1}{64} \cdot \int 1 + \frac{7}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{64} (\int 1 d u + \int \frac{7}{u} d u)

\int 1 d u = u

\int \frac{7}{u} d u = 7 ln ∣ u ∣

= \frac{1}{64} (u + 7 ln ∣ u ∣)

Setze in

u = 8 x - 7

ein

= \frac{1}{64} (8 x - 7 + 7 ln ∣ 8 x - 7 ∣)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{64} (8 x - 7 + 7 ln ∣ 8 x - 7 ∣) + C

\frac{\partial}{\partial z} (6 x^{\frac{y}{z}})

in v erse l a pl a ce \frac{1}{s + 3} - \frac{1}{s + 4}

\frac{\partial}{\partial s} (\frac{( 2 r + s )}{t})

\frac{d}{d y} (x sin (x y))

x \to 1 lim (\frac{1}{x - 2})