CalculusAdditional / Further Maths

Integrating powers of linear expressions

Integrate a power of a linear expression without expanding it.

  • for and .
  • Keep the inner expression unchanged. Divide by its derivative as well as the new power.
  • This includes negative and fractional powers wherever the expression is defined.

Example 1

Integrate with respect to . Work where .

The inner derivative is constant.Divide by the inner derivative and the new exponent.

Example 2

Integrate with respect to . Work where .

The inner derivative is constant.Divide by the inner derivative and the new exponent.

Your turn

Question 1

Integrate with respect to . Work where .

Check answer
The inner derivative is constant.Divide by the inner derivative and the new exponent.
Question 2

Integrate with respect to . Work where .

Check answer
The inner derivative is constant.Divide by the inner derivative and the new exponent.
Question 3

Integrate with respect to . Work where .

Check answer
The inner derivative is constant.Divide by the inner derivative and the new exponent.
Question 4

Integrate with respect to . Work where .

Check answer
The inner derivative is constant.Divide by the inner derivative and the new exponent.
Question 5

Integrate with respect to . Work where .

Check answer
The inner derivative is constant.Divide by the inner derivative and the new exponent.
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