When can I use the natural log to help solve an integral? Why is it okay to do this: int 1/(x-2)dx =ln(x-2) but not this: int 1/(1-x^2)dx=ln(1-x^2)

Jared Lowe

Jared Lowe

Answered question

2022-11-15

When can I use the natural log to help solve an integral?
Why is it okay to do this: 1 x 2 d x = ln ( x 2 )
but not this: 1 1 x 2 d x = ln ( 1 x 2 )

Answer & Explanation

cenjene9gw

cenjene9gw

Beginner2022-11-16Added 13 answers

The chain rule is the difference. Note that d u u = ln | u | . So, you must have a fraction of the form u on the bottom and the derivative of u on the top. For your second example, u = 1 x 2 , but d u = 2 x d x is not the numerator.
Nico Patterson

Nico Patterson

Beginner2022-11-17Added 3 answers

Because the derivative of ln ( f ( x ) ) is not 1 f ( x ) for all differentiable function f, even if it is true for f ( x ) = x a where a is a constant.
The derivative of ln ( f ( x ) ) is f ( x ) f ( x ) applying the chain rule.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?