Problem 1
(Fill in the Blank): Integrate by parts to evaluate the integral. For full credit, please show your
calculations.
$\int xe^{5x} dx$ = <your answer here>
Problem 2
(Fill in the Blank): Integrate by parts to evaluate the integral. For full credit, please show your
calculations.
$\int \sqrt{t} \ln t \, dt$ = <your answer here>
Problem 3
(Fill in the Blank): Integrate by parts to evaluate the integral. For full credit, please show your
calculations.
$\int 3x^2 \tan^{-1}(x) \, dx$ = <your answer here>
Problem 4
(Fill in the Blank): Use trigonometric identities and integrate by substitution to evaluate the
integral. For full credit, please show your calculations.
$\int \cos^5(\frac{x}{5})\sin^4(\frac{x}{5}) \, dx$ = <your answer here>