Integrating reciprocals and logarithms Revision Card

CalculusAdditional / Further Maths

Recognise when an integral gives a logarithm.

.
for .
Work on an interval where the denominator is nonzero. Do not use the power rule with exponent .

Example 1

Integrate with respect to , on an interval where .

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.

Integrate with respect to , on an interval where .

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.

Question 1

Integrate with respect to , on an interval where .

Check answer

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.

Question 2

Integrate with respect to , on an interval where .

Check answer

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.

Question 3

Integrate with respect to , on an interval where .

Check answer

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.

Question 4

Integrate with respect to , on an interval where .

Check answer

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.

Question 5

Integrate with respect to , on an interval where .

Check answer

Find the denominator’s derivative.

Divide by the inner derivative; use a logarithm with an absolute value.