Evaluate the following indefinite integrals. (1-4)

1. \( \displaystyle \int \sqrt{x}(x+3\sqrt{x}) \)

Solution

2. \( \displaystyle \int \frac{2\sin^2 x+5\cot{x}}{3\sin{x}} \;dx \)

Solution

3. \( \displaystyle \int (x-3)^2 \;dx \)

Solution

4. \( \displaystyle \int \frac{4}{1+x^2} \;dx \)

Solution

5. The velocity function for a moving particle at time \( t\) is \( v(t)= 3t-9 \) meters per second.

(a) Find the displacement of the particle during \( 1\leq t\leq 4\)

Solution

(b) Find the total distance traveled during \( 1\leq t \leq 4 \).

Solution