What is the antiderivative of (x+2)/(x+1) dx?

Antiderivative is $\int \left(\frac{x + 2}{x + 1}\right) \mathrm{dx} = x + \ln \left(x + 1\right) + C$

Explanation:

Antiderivative is the same as finding the indefinite integral of a given differential

$\int \left(\frac{x + 2}{x + 1}\right) \mathrm{dx} = \int \left(\frac{x + 1 + 1}{x + 1}\right) \mathrm{dx} = \int \left(\frac{x + 1}{x + 1} + \frac{1}{x + 1}\right) \mathrm{dx}$

$\int \left(\frac{x + 2}{x + 1}\right) \mathrm{dx} = \int \left(\frac{x + 1}{x + 1}\right) \mathrm{dx} + \int \left(\frac{1}{x + 1}\right) \mathrm{dx}$

$\int \left(\frac{x + 2}{x + 1}\right) \mathrm{dx} = \int \mathrm{dx} + \int \left(\frac{1}{x + 1}\right) \mathrm{dx}$

$\int \left(\frac{x + 2}{x + 1}\right) \mathrm{dx} = x + \ln \left(x + 1\right) + C$

God bless....I hope the explanation is useful.