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

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Answer 1 · 2016-02-20T17:18:17

Use substitution.

$int_1^e (2)/(2x+5) * dx = int_1^e 1/(2x+5) 2 dx$

Let $u = 2x+5$ so $du = 2dx$ and

when $x=1$ , $u=7$ and

when $x=e$ , $u = 2e+5$

$int_1^e 1/(2x+5) 2 dx = int_7^(2e+5) 1/u du$

$= lnu]_7^(2e+5)$

$= ln(2e+5)-ln7$

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