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

1 Answer
Oct 16, 2015

#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#