2x-1-x-

Question Number 92137 by hore last updated on 05/May/20

\int \frac{2 x}{1 + x}

Commented by john santu last updated on 05/May/20

\int \frac{2 x d x}{x + 1} = \int \frac{2 (x + 1) - 2}{x + 1} d x

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

= 2 x - 2 \ln ∣ x - 1 ∣ + c

Commented by Rio Michael last updated on 07/May/20

\frac{2 x}{1 + x} = 2 - \frac{2}{x + 1} [can use long division]

\int \frac{2 x}{1 + x} d x = \int (2 - \frac{2}{x + 1}) d x = 2 x - 2 \ln (x + 1) + C