Life's not easy
- SUBSTITUTE by choosing u = g (x) and write du = g' (x) dx = (du / dx) = dx. Then subsitute both u and du to the original integral producing a new integral in the form of f(u).
- ANTIDIFFERENTIATE in terms of u. F ' (u) = f (u)
- RESUBSTITUTE g(x) to obtain the antiderivative in terms of x.
The method of INTEGRATION BY PARTS:
And the NUMERICAL INTEGRATION
- the MIDPOINT RULE
- the TRAPEZOID RULE
- and the SIMPSON SUM (where twice the value of the MIDPOINT is added to the TRAPEZOID value all over 3)