Partial fractions checklist:

• Ensure deg(P) < deg(Q)
• Factor Q completely
• Repeated factors need stacked terms
• Cover-up method for distinct linear factors

Standard integrals — memorize all 6 forms involving 1/(x^2+/-a^2) and sqrt variants

Trig substitution — match sqrt type:

• sqrt(a^2-x^2) => x = a sin(theta)
• sqrt(a^2+x^2) => x = a tan(theta)
• sqrt(x^2-a^2) => x = a sec(theta)

Reduction formulas — key base cases:

• sin^0 = x, sin^1 = -cos x
• tan^0 = x, tan^1 = ln|sec x|
• sec^0 = x, sec^2 = tan x

Wallis — remember: pi/2 only for even n

e^x pattern: integral e^x[f+f'] = e^x*f + C

Common mistakes to avoid:

• Forgetting long division before partial fractions
• Wrong sign in trig substitution dx
• Missing pi/2 in Wallis for even n
• Wrong base case in reduction formula
• Not verifying answer by differentiation