CalculusAdditional / Further Maths

Integrating negative powers

Rewrite reciprocals as powers before integrating.

  • Rewrite a reciprocal as a negative power: .
  • Use when .
  • For use . Work on an interval excluding zero.

Example 1

Integrate with respect to . Assume .

Rewrite the denominator as a negative power.Increase the power and divide by the new power.

Example 2

Integrate with respect to . Assume .

Rewrite the denominator as a negative power.Increase the power and divide by the new power.

Your turn

Question 1

Integrate with respect to . Assume .

Check answer
Rewrite the denominator as a negative power.Increase the power and divide by the new power.
Question 2

Integrate with respect to . Assume .

Check answer
Rewrite the denominator as a negative power.Increase the power and divide by the new power.
Question 3

Integrate with respect to . Assume .

Check answer
Rewrite the denominator as a negative power.Increase the power and divide by the new power.
Question 4

Integrate with respect to . Assume .

Check answer
Rewrite the denominator as a negative power.Increase the power and divide by the new power.
Question 5

Integrate with respect to . Assume .

Check answer
Rewrite the denominator as a negative power.Increase the power and divide by the new power.
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