Strategy Summary for Integration
 Step 1: Simplify the integrand as much as possible. Sometimes a daunting integral can be made to be extremely simple with some algebraic simplification. For example, consider integrating the function $f(x) = \frac{x + 2}{x + 1}$. Integrating this example isn't particularly hard, however, notice that $f(x) = \frac{(x + 1) + 1}{(x+ 1)} = 1 + \frac{1}{x + 1}$. Integrating $f(x)$ now is even simpler!
 Step 2: Look for an easy u-substitution. U-substitution is probably one of the easier techniques to apply, so it is definitely a first choice if it is easy to apply. For example, integrating the function $f(x) = \frac{x + 1}{x^2 + 1}$ can be tackled on more easily by making the substitution $u = x^2 + 1$ so that $du = 2x \: dx$.