SOLUTIONS CHAPTER 16.4
MATH 132  WI00
What I’ll do in the following.
.. since you are now skilled in computing integrals
... will be just give you the idea (the
u
, that is) and the result you should get. Mind
the fact that you might follow a diFerent method (there’s no mathematics problem
that admits only one solution!!), and you might get a
diferent looking result

then your job will also be to check your answer :), since the answers should be the
same.
6.
Take
u
=
e
x
2

2.
Reasons:
•
taking just
x
2
is not enough (try it!), so this would be the next step
•
this
u
combines a constant too  always take the expression that has constants
in it for
u
, since by diFerentiation it will vanish (as opposed to NOT showing up
after diFerentiation)
Result:
1
2
ln(
e
x
2

2) +
C
•
12.
We can use the
u
trick here, but with a twist!
Since we have
x

5 as the denominator, and we cannot really get rid of it, the
one thing we can do to simplify our work is to call it
u
:
u
=
x

5
⇒
du
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 Spring '08
 Staff
 Calculus, Integrals, Natural logarithm, Logarithm, ln ln

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