Question

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

Answer 1

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

Explanation:

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`