PROOF:
so that
But
In a is a constant, so
Then,
by dividing both sides by In a:
or
where
EXAMPLE: Evaluate
SOLUTION: Let
so that
Therefore,
by knowing that
^{}
and
using substitution, we find that
EXAMPLE: Evaluate
SOLUTION. Let
so that
The integral should contain a factor of 2. Thus we
insert a factor of 2 in the integral and compensate by multiplying the integral
by 1/2.
Then,
Therefore,
_{}
EXAMPLE: Evaluate
SOLUTION: Let
so that
We
find we need 2x dx; therefore, we remove the 7 and insert a 2 by writing
PRACTICE
PROBLEMS: Evaluate the following integrals:
ANSWERS:
