CPM Homework Help : CALC Problem 6-158

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6-158.

Use the relationship between differentiation and integration to simplify the following problems.

Hint:

As you work through this set of problems, look for patterns.

$\frac { d } { d x } ( \operatorname { cos } ( 3 x ^ { 2 } ) )$
Hint (a):
Chain Rule.

$\int 6 x \operatorname { sin } ( 3 x ^ { 2 } ) d x$
Hint 1(b):
This one is tricky. Concentrate on the $3x^²$ part of the integrand. What will happen when you anti-differentiate that part?
Hint 2(b):
Refer to part (a) (the question, not the hint).

$\frac { d } { d x } ( \sqrt { 3 x ^ { 9 } - 5 x } )$
Hint (c):
Before you differentiate, rewrite the expression as with a fractional exponent.

$\int \frac { 27 x ^ { 8 } - 5 } { \sqrt { 3 x ^ { 9 } - 5 x } } d x$
Hint (d):
A clue is directly above (in part (c)).
And don't forget the $+C$ .

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