CPM Homework Help : CALC3RD Problem 7-102

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Home > CALC3RD > Chapter Ch7 > Lesson 7.3.1 > Problem 7-102

7-102.

No calculator! Integrate.

$\int ( 3 e ^ { 4 x } + 2 ^ { x } ) d x$
Hint (a):
$e$ is NOT a variable.

$\int _ { 0 } ^ { \pi } \operatorname { sin } ^ { 3 } ( x ) \operatorname { cos } ( x ) d x$
Step (b):
Let $u=\sin\left(x\right)$ .

$\int x ^ { 2 } ( 3 x ^ { 3 } + 5 ) ^ { 4 } d x$
Hint (c):
Notice that the term in parentheses has a highest-power of $3$ , while the term outside of the parenthesis has a power of $2$ .
$U$ -substitution!

$\int \frac { 5 x ^ { 0.25 } } { 4 x ^ { 1.25 } - 6 } d x$
Hint (d):
Refer to the hint in part (c).

$\int _ { e } ^ { e ^ { 3 } } \frac { 1 } { x } \operatorname { ln } ( x ) d x$
Hint (e):
What is the derivative of $\ln\left(x\right)$ ?

$\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } d x$
Hint (f):
Inverse trig.

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