Mathematics - Calculus - Integral - Integration techniques - U-Substitution and Integration by Parts

12 steps: (1) U-SUBSTITUTION: reverse of chain rule. (2) If integrand has f(g(x))·g'(x), let u=g(x), du=g'(x)dx. (3) Example: ∫2x·cos(x²)dx. Let u=x², du=2xdx. = ∫cos(u)du = sin(u)+C = sin(x²)+C. (4) Example: ∫x/(x²+1)dx. Let u=x²+1, du=2xdx. = (1/2)∫du/u = (1/2)ln|u|+C = (1/2)ln(x²+1)+C. (5) Key: l