CalculusAdditional / Further Maths

Integrating fractional powers

Integrate roots and reciprocal roots using fractional powers.

  • Write roots as powers, such as and .
  • Add one to the exponent, then divide by the new exponent.
  • For example, . Check the real domain.

Example 1

Integrate with respect to . Assume .

Write the root as a fractional power.Add one to the power and divide.

Example 2

Integrate with respect to . Assume .

Write the root as a fractional power.Add one to the power and divide.

Your turn

Question 1

Integrate with respect to . Assume .

Check answer
Write the root as a fractional power.Add one to the power and divide.
Question 2

Integrate with respect to . Assume .

Check answer
Write the root as a fractional power.Add one to the power and divide.
Question 3

Integrate with respect to . Assume .

Check answer
Write the root as a fractional power.Add one to the power and divide.
Question 4

Integrate with respect to . Assume .

Check answer
Write the root as a fractional power.Add one to the power and divide.
Question 5

Integrate with respect to . Assume .

Check answer
Write the root as a fractional power.Add one to the power and divide.
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