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

Answer 1

Isabella Ackerman

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

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.

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Answer 2

Isabella Ackerman

The antiderivative of (\frac{x+2}{x+1}) with respect to (x) is ((x+2)\ln|x+1| + C), where (C) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.