Question

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

Answer 1

Antiderivative is `int((x+2)/(x+1))dx=x+ln(x+1)+C`

Explanation:

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

`int ((x+2)/(x+1))dx=int((x+1+1)/(x+1))dx=int((x+1)/(x+1)+1/(x+1))dx`

`int ((x+2)/(x+1))dx=int((x+1)/(x+1))dx+int(1/(x+1))dx`

`int ((x+2)/(x+1))dx=int dx+int(1/(x+1))dx`

`int ((x+2)/(x+1))dx=x+ln (x+1)+C`

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