# How do you evaluate the definite integral #int (2)/(2x+5) * dx# from #[1, e]#?

Use substitution.

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To evaluate the definite integral ∫(2)/(2x+5) dx from 1 to e:

- Find the antiderivative of the function (2)/(2x+5) with respect to x, which is ln|2x+5| + C.
- Evaluate the antiderivative at the upper limit of integration (e) and subtract the value of the antiderivative at the lower limit of integration (1).
- Substitute the upper limit (e) into the antiderivative: ln|2(e)+5| = ln|2e+5|.
- Substitute the lower limit (1) into the antiderivative: ln|2(1)+5| = ln|7|.
- Subtract the value at the lower limit from the value at the upper limit: ln|2e+5| - ln|7|.
- Simplify: ln| (2e+5) / 7 |. This is the value of the definite integral.

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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.

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.

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.

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