# Worksheet: Reduction Formulae for Integration

In this worksheet, we will practice deriving reduction formulae and using them to evaluate integrals.

Q1:

Reduction formulas relate integrals involving an integer parameter. Let for .

What is ?

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Use , and integration by parts to derive a relation between and . Clear denominators if necessary.

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From your previous answer, find a formula for in terms of .

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Evaluate the indefinite integral .

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Q2:

The following table lists the integrals for , and 2.

 𝑛 𝐼 0 1 2 𝑥(𝑥−1)+𝐾ln 14𝑥(2𝑥−1)+𝐾ln 19𝑥(3𝑥−1)+𝐾ln

Use the table to predict a formula for and then verify this by differentiating.

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Write the and with which you can prove the formula using integration by parts.

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Q3:

Evaluate the indefinite integral .

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Q4:

Evaluate the indefinite integral .

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Q5:

Evaluate the indefinite integral .

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