Evaluate each of the following integrals without a calculator.

1. $\int_{ }^{ }\sin(17x)dx$ 

   Answer (a):

   $k\cos\left(17x\right)+C$
   What is $k$?

2. $\int _ { 1 } ^ { 4 } \frac { 5 } { \sqrt { x } } d x$ 

   Hint (b):

   $\frac{5}{\sqrt{x}}= 5x^{-1/2}$

3. $\int _ { - 2 } ^ { 1 } \frac { 24 } { \sqrt { x + 3 } } d x$ 

   Answer (c):

   $48$

4. $\int ( 9 x + 4 x ^ { 3 } ) d x$ 

   Hint (d):

   'Undo' the Power Rule.