Completing the Square Inside an Integral Worksheet with Answer Key

What's on the worksheet

1. Complete the square in each denominator, then find the integral.
   \displaystyle\int \dfrac{dx}{x^2 - 10x + 26}\displaystyle\int \dfrac{7}{x^2 + 4x + 53}\,dx\displaystyle\int \dfrac{dx}{x^2 - 5x + 8}\displaystyle\int \dfrac{dx}{16x^2 + 8x + 10}
2. Find each integral and give the interval on which your answer holds.
3. Split the numerator into a multiple of the derivative of the denominator plus a constant, then find 4x - 15x² - 10x + 29\,dx.
4. Evaluate _-2² dxx² + 2x + 4 exactly.
5. The quadratic 6x - x² - 13 opens downward.
6. In a made-up model, the water refill station at a state park campground dispenses water at the rate r