Pattern 1: Partial fraction integration (High frequency) Decompose rational functions and integrate. Often combined with definite integration limits. Key: don't forget long division for improper fractions.

Pattern 2: Standard form integrals (High frequency) Integrals reducible to $\frac{dx}{x^2+a^2}$, dx/sqrt(a^{2-x}^2), etc. after completing the square. Quick recognition saves time.

Pattern 3: Wallis/reduction formula values (Moderate) Direct application of Wallis' formula for integral$\frac{0 to pi}{2}$ $sin^n$ or $cos^n$. Know the pattern: even n has pi/2, odd n doesn't.

Pattern 4: $e^x$[f+f'] type (Moderate) Recognize the pattern in disguised forms. Common: e^x$$\frac{(x-1}{x}^2) = $e^x$(1/x - 1/$x^2$).

Pattern 5: Trigonometric substitution (Moderate) For sqrt(quadratic) integrals. Complete the square first, then apply standard substitution.

Pattern 6: Integration by parts (High frequency) ln(x), arctan(x), arcsin(x) multiplied by polynomials. LIATE rule determines the setup.

Pattern 7: Non-obvious substitutions (Low-Moderate) x+1/x or x-1/x for $\frac{x^2+/-1}{(x^4+1)}$ type. Recognizing these saves significant time.