Problem

PART 1: Fill in the blanks.

• Work need not be shown, only answers will be graded.

• 4 points for each blank and 100 points total.

• Each answer need to be clearly labeled on the answer sheet.

• Use of any device with computer algebra system during the exam will result in zero points.

5. Calculate the following integrals:

• $\displaystyle\int_{0}^{2}\frac{x^3}{(x^2+4)^3}\,dx=\underline{\quad(6)\quad}$.
• $\displaystyle\int_{0}^{\ln 2}\sqrt{e^x-1}\,dx=\underline{\quad(7)\quad}$. (Hint: Use $u=\sqrt{e^x-1}$.)
• $\displaystyle\int_{1}^{3}\frac{x-2}{\sqrt{x^2-1}}\,dx=\underline{\quad(8)\quad}$.