integral of (ln(x+4))/(x^2)

Lösung

\int \frac{ln ( x + 4 )}{x ^{2}} d x

- \frac{ln ( x + 4 )}{x} + \frac{1}{4} ln ∣ x ∣ - \frac{1}{4} ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{ln ( x + 4 )}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{ln ( x + 4 )}{x} - \int - \frac{1}{x ( x + 4 )} d x

\int - \frac{1}{x ( x + 4 )} d x = - \frac{1}{4} ln ∣ x ∣ + \frac{1}{4} ln ∣ x + 4 ∣

= - \frac{ln ( x + 4 )}{x} - (- \frac{1}{4} ln ∣ x ∣ + \frac{1}{4} ln ∣ x + 4 ∣)

Vereinfache

= - \frac{ln ( x + 4 )}{x} + \frac{1}{4} ln ∣ x ∣ - \frac{1}{4} ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{ln ( x + 4 )}{x} + \frac{1}{4} ln ∣ x ∣ - \frac{1}{4} ln ∣ x + 4 ∣ + C

\frac{d}{d x} (9 + 4 x)

\frac{\partial}{\partial x} (2 cos (x + 2 y))

d er i v a t i v e x^{2} sin^{4} (x) + x cos^{- 2} (x)

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

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