Question 1157386: Solve this indefinite integral ∫ 6dx/〖x(3x+1)〗by using the following formula:
∫ dx/(x(mx+b))=1/b In |x/(mx+b)|
Found 3 solutions by KMST, ikleyn, math_tutor2020:
Answer by KMST(5434)   (Show Source):
You can put this solution on YOUR website! The formula is
     , where  is the function natural logarithm.
The indefinite integral to solve is
 which is equal to  ,
as anyone starting to learn about indefinite integrals in calculus class would know.
We notice that turns into  for  .
So, applying the given formula, we confidently write
  
IMPORTANT NOTE:
When we write  on paper, it does mean dx/[x(mx+b)],
and we do not need the square bracket around  ,
because that horizontal line between  and comes with invisible brackets around the expressions above and under it.
That horizontal line is a grouping symbol, just like the square root symbol.
However, when we have to type expressions in one line we need the extra brackets.
If you try to key  into a calculator,
you must type as (0.723-0.002)/(0.745-0.001).
If you skip the brackets, almost all calculators will calculate
    ,
because modern calculators use algebraic language, and know the conventions about order of operations.
Answer by ikleyn(54018)  (Show Source):
Answer by math_tutor2020(3847)  (Show Source):
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