CalculusAdditional / Further Maths

Simplifying before integration

Expand or simplify an expression before integrating.

  • Expand brackets or divide every numerator term by the denominator first.
  • Then integrate the resulting sum term by term.
  • You cannot integrate a product by multiplying the integrals of its factors.

Example 1

Integrate with respect to .

Simplify the expression before integrating.Use the power rule term by term.

Example 2

Integrate with respect to . Assume .

Simplify the expression before integrating.Use the power rule term by term.

Your turn

Question 1

Integrate with respect to .

Check answer
Simplify the expression before integrating.Use the power rule term by term.
Question 2

Integrate with respect to . Assume .

Check answer
Simplify the expression before integrating.Use the power rule term by term.
Question 3

Integrate with respect to .

Check answer
Simplify the expression before integrating.Use the power rule term by term.
Question 4

Integrate with respect to . Assume .

Check answer
Simplify the expression before integrating.Use the power rule term by term.
Question 5

Integrate with respect to .

Check answer
Simplify the expression before integrating.Use the power rule term by term.