# Worksheet: Integration by Partial Fractions with Linear Factors

In this worksheet, we will practice using partial fractions to evaluate integrals of rational functions with linear factors.

**Q5: **

Use partial fractions to find an analytic expression for the integral

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**Q7: **

Consider the function which is defined on .

Find an antiderivative of such that . What is ?

- A, .
- B, .
- C, .
- D, .
- E, .

Is it possible to find an antiderivative that satisfies , where ? If so, what is ?

- AYes,
- Bno

What you have found above seems to violate the result that says that any two antiderivatives must differ by a constant function, because is not a constant function. Why is there no contradiction?

- Abecause that result assumes that the domain is an interval
- Bbecause is constant; it has the value 0 on and the value 1 on
- Cbecause that result only holds sometimes; sometimes it fails
- Dbecause neither nor is differentiable; that result only applies to differentiable functions
- Ebecause that result requires additional conditions to the antiderivatives

**Q13: **

Use partial fractions to evaluate the integral .

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**Q14: **

Use partial fractions to evaluate the integral .

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- E