# Problem 1: Evaluate the integral Z x 2 − x + 1 x − ...

## Transcribed Text

Problem 1: Evaluate the integral Z x 2 − x + 1 x − 2 dx using polynomial long division. a.) Use long division to break apart the integrand into a polynomial and a remainder. b.) Evaluate the broken up integrand you found above. Problem 2: Rewrite the integrand of the integral Z 1 x 2 + 3x − 3 dx by completing the square. a.) Complete the square for the polynomial in the denominator. b.) (Extra) Use a trigonometric substitution to evaluate the integral (Hint: use two successive u-subs). 1 2 Problem 3: Determine whether the following statements are true or false and give an explanation or counterexample: a.) Z uv0 dx = Z udx Z v 0 dx . b.) Z uv0 dx = uv − Z vu0 dx. c.) Z vdu = uv − Z udv. Problem 4: Evaluate the integral Z π 0 x cos(x)dx: Problem 5: Evaluate the integral Z x ln2 (x)dx: Problem 6: Use trigonometric identities to evaluate the integral Z sin3 (x) cos2 (x)dx: Problem 7: Use a trigonometric substitution to evaluate the integral Z x 2 16 + x 2 dx:

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