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 $\frac{1}{x^2+/-a^2}$ 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