integral of ln(x/(x+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int_{0}^{4} x^{2} - 4 x + 3 d x

\frac{d}{d x} (d - b - a x - \frac{d}{x ^{2}})

d er i v a t i v e 9 x

d er i v a t i v e f (x) = 4 sin (x) + 7 cos (x)

\frac{\partial}{\partial x} (x^{4} sin (x y^{3}))