Question

Evaluate
∫2x+1 /x(x+1) dx​

Answer 1

Answer:

$\sf{ln|x + 1| + ln |x|\: + C}$

Step-by-step explanation:

$\int \frac{2x + 1}{x(x + 1)} dx \\ \\ \int \frac{x + ( x + 1) }{x(x + 1)} dx \\ \\ \int \frac{x}{x(x + 1)} dx + \int \frac{(x + 1)}{ x(x + 1)} dx \\ \\ \int \frac{1}{x + 1} dx + \int \frac{1}{x} dx \\ \\ \sf{ln|x + 1| + ln |x|\: + C }$

Integration of f(ax + b) is F(ax + b)/a, as happened in integration of 1/(x + 1).

Int. of 1/(x + 1) = ln|x + 1|/1 = ln|x + 1|