Simplifying Calculus: Spotting Patterns

You are definitely overcomplicating your calculus homework. Solving integrals is actually just

using a cheat sheet of patterns. When you see tangents and secants, look at the exponents

immediately. If the secant power is even, save a secant squared and substitute tangent.

If the tangent power is odd, pull out a secant-tangent. It is automatic. For those impossible

square roots, use trig substitution. If you see a number minus x squared, turn that x into

a sine function and watch the root disappear. And for giant fractions, just smash them

into smaller pieces with partial fractions. Stop panicking and start spotting the patterns.