Integration by Substitution is a procedure that at first may look too long to complete, but, with a little exposure, much of the time, may be completed mentally.

      The integrand must have these as "factors"

• dx, the differential of x
• an "outer function" evaluated at an "inner function,"
• the derivative of the "inner function," and
• may be off by a constant -- need a constant or have an extra constant factor.

      The strategy is to:

• rewrite the integral using a new independent variable, u, to replace the more complicated original independent variable, x,
• then complete the easier integration,
• then replace the u with the x if needed.

      On this page computation is shown in two areas, the intergal equations and the computation with u.