What is the integral of x/(x+2y) ?

The integral of x/(x+2y) is (x^2)/(x+2y)-2y(ln|x+2y|+(2y)/(x+2y))+C

Popular >

integral of x/(x+2y)

\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

Solution steps

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

Apply Integration By Parts

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

= \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})

Add a constant to the solution

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

\frac{x ^{2} - 1}{x ^{3}}

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

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))

What is the integral of x/(x+2y) ?
The integral of x/(x+2y) is (x^2)/(x+2y)-2y(ln|x+2y|+(2y)/(x+2y))+C