Replacing 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,
In general, if F'(x) = f(x) then for any m ≠ 0,
cos θ dθ = sin θ + c hence cos 2θ dθ = ½sin 2θ + c.
e4x+5 dx = ¼e4x+5 + c
dx = ln |(6x−10)| + c
Do plenty of exercises until you feel confident with linear substitutions.
Now try some exercises that involve use of the multiple rule too.