


IntegrationLinear SubstitutionReplacing the variable x in each of the basic functions, such as cos x, by a linear expression mx + b, we get another function, cos(mx+b). By the Chain Rule for differentiation, we see that, Hence In general, if F'(x) = f(x) then for any m ≠ 0, Examplescos θ dθ = sin θ + c hence cos 2θ dθ = ½sin 2θ + c. e^{4x+5} dx = ¼e^{4x+5} + c dx = ln (6x−10) + c ExerciseDo plenty of exercises until you feel confident with linear substitutions. Now try some exercises that involve use of the multiple rule too. 