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In this lesson, we will learn how to use partial fractions for rational functions with linear factors to evaluate their integration.
Q1:
Use partial fractions to evaluate 𝑥 + 4 𝑥 + 1 ( 𝑥 − 1 ) ( 𝑥 + 1 ) ( 𝑥 + 3 ) 𝑥 2 d .
Q2:
Use partial fractions to evaluate 6 𝑥 + 7 ( 𝑥 + 2 ) 𝑥 2 d .
Q3:
Use partial fractions to evaluate 1 ( 𝑥 − 1 ) 𝑥 2 2 d .
Q4:
Use partial fractions to evaluate 𝑥 ( 𝑥 − 1 ) ( 𝑥 + 2 𝑥 + 1 ) 𝑥 2 2 d .
Q5:
Use partial fractions to find an analytic expression for the integral
Q6:
Find 𝐹 so that 𝐹 ′ ( 𝑥 ) = 𝑥 ( 𝑥 − 𝑒 ) 2 and 𝐹 ( 0 ) = 2 .
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