How do you find the indefinite integral of $1/2int (2/(2x+5))dx$ ?

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Answer 1 · 2015-10-16T21:14:38

$1/2int2/(2x+5)dx=1/2ln|2x+5|+C$

If we use substitution and let $u=2x+5$ , then the differential $du=2dx$ and so $1/2du=dx$

We may then write this original integral in terms of u as follows :

$2/2*1/2int1/u du$

This may be evaluated by rules of integration as $1/2ln|u|+C$ .

Now substituting back to x we get the final answer as $1/2ln|2x+5|+C$

How do you find the indefinite integral of 1/2int (2/(2x+5))dx1/2int (2/(2x+5))dx?