9 methods · 36 worked questions using these methods
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The power rule only applies to terms xk. Before integrating, expand brackets and squares, split fractions term by term, and rewrite roots and reciprocals as fractional or negative powers so every term is integrable directly.
Trigger: an integrand that is a product, a square, a quotient, or contains x or 1/xn.
Instances: (i) split a single fraction over several numerator terms, e.g. (3−2x)/x3/2=3x−3/2−2x−1/2; (ii) expand a square such as (x2−4/x2)2 into separate power terms; (iii) cancel a factor first with a difference of two squares, e.g. (t−1)/(1+t)=t−1.
