Topic overview
The most common unfamiliarity in integration questions comes from the method not being stated. First observe derivative pairings, degree differences, radicals and splittable structures, then choose among substitution, integration by parts and algebraic manipulation.
Key concepts
On seeing consider logarithms; for a polynomial times an exponential or trigonometric function consider integration by parts; and radicals often suggest a trigonometric substitution. When changing variables in a definite integral you must change the limits at the same time.
Key points
- ◆Write out the substitution and the differential clearly
- ◆The choice made in integration by parts affects the length of the computation
- ◆A definite integral does not retain the original variable in the final answer
Worked examples
Try each example yourself before checking the explanation.
1Hidden logarithmic type
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