Use Integration by Substitution to Undo:
· Taking the Derivative of a Composition of Functions,
· The Chain Rule for Taking Derivatives.
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.
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