Mistake 1: Forgetting to perform long division before partial fractions when deg(P) >= deg(Q).

Mistake 2: In partial fractions with repeated factors, writing $\frac{A}{x-a}$ instead of $\frac{A}{x-a}$ + $\frac{B}{x-a}$^2 for (x-a)^2 factor.

Mistake 3: Sign errors in trigonometric substitution. Remember: if x = a sin(theta), then dx = a cos(theta) d(theta), and sqrt(a^{2-x}^2) = a cos(theta) (not a sin(theta)).

Mistake 4: In reduction formulas, using the wrong base case. $I_0$ for $sin^n$ is x (not 1), and $I_1$ is -cos(x) (not cos(x)).

Mistake 5: Forgetting the pi/2 factor in Wallis' formula for even n. Odd n does NOT include pi/2.

Mistake 6: In $e^x$[f+f'] type, incorrectly splitting the integrand. Always verify by differentiating your answer.