## Transcribed Text

1. Find the partial fraction decomposition for the rational function
x2-x+5
x³+x
2. Use the partial fraction decomposition of the function to evaluate the integral
x+5
Solving using a formula is not acceptable.
3. Evaluate each of the following integrals, using a trigonometric substitution. Do not
forget the back substitution. Solving using other methods is not acceptable.
(a) I dx
2 +9
16 1 dx
(c) S x²-4 x dx
4. First complete the square, make the appropriate substitutions, and then evaluate the
integral:
I
2 + 5
5. Evaluate each of the following integrals, using the given substitution or identity.
Solutions using other methods are not acceptable.
(a) cos³ xsin4 xdx
(substitution " = sin x & identitycosx+sinx=1)
(substitution u = tan x &identitysec²x=l+tan2x) = =
(c)
I sin(5x)sin(3x)dx
- +
(d)
I
cos 6x cos 4xdx
- +

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.