integral of x/(x+2y)

Lösung

\int \frac{x}{x + 2 y} d x

\frac{x ^{2}}{x + 2 y} - 2 y (ln ∣ x + 2 y ∣ + \frac{2 y}{x + 2 y}) + C

Schritte zur Lösung

\int \frac{x}{x + 2 y} d x

Wende die partielle Integration an

= \frac{x ^{2}}{x + 2 y} - \int \frac{2 y x}{( x + 2 y ) ^{2}} d x

\int \frac{2 y x}{( x + 2 y ) ^{2}} d x = 2 y (ln ∣ x + 2 y ∣ + \frac{2 y}{x + 2 y})

= \frac{x ^{2}}{x + 2 y} - 2 y (ln ∣ x + 2 y ∣ + \frac{2 y}{x + 2 y})

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{x + 2 y} - 2 y (ln ∣ x + 2 y ∣ + \frac{2 y}{x + 2 y}) + C

\frac{d v}{d t} = 2.1 - \frac{7 v}{2180}, v (0) = 0

t an g e n t f (x) = - 2 x^{3}, at x = 2

\frac{d}{d z} (\frac{z ^{2}}{( z - 2 i ) ^{2}})

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

\int \frac{x arctan ( x )}{( 1 + x ^{2} ) ^{2}} d x