Integration by Substitution

Task goals

• Foundation: Integrate a simple composite function such as (ax+b)^n or e^{ax+b} using a given or obvious linear substitution u = ax+b.
• Proficient: Choose an appropriate substitution for a composite function (including trig or rational integrands), correctly transform dx into du, integrate, and reverse the substitution to express the answer in terms of the original variable.
• Excellence: Apply integration by substitution to evaluate definite integrals by changing the limits into u-values, and to solve less obvious substitutions requiring algebraic manipulation before or after substituting.