No Calculator! Integrate.

1. $\int ( 3 e ^ { 4 x } + 2 ^ { x } ) d x$

   Hint (a):

   Careful. $e$ is NOT a variable.

2. $\int _ { 0 } ^ { \pi } ( \operatorname { sin } ^ { 3 } x \operatorname { cos } x ) d x$

   Step (b):

   Let $u =\operatorname{sin}x$.

3. $\int x ^ { 2 } ( 3 x ^ { 3 } + 5 ) ^ { 4 } d x$

   Hint (c):

   Notice that the term in parentheses has a highest-power of$x^³$, while the term outside of the parenthesis has a power of $x^²$.
   $U$-substitution!

4. $\int \frac { 5 x ^ { 0.25 } } { 4 x ^ { 1.25 } - 6 } d x$

   Hint (d):

   Refer to the hint in part (c).

5. $\int _ { e } ^ { e ^ { 3 } } \frac { 1 } { x } \operatorname { ln } x d x$

   Hint (e):

   What is the derivative of $y =\operatorname{ln}x$?

6. $\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } d x$

   Hint (f):

   Inverse trig.