integration-by-substitution-antiderivatives

Calculus: We introduce the technique of integration by substitution for indefinite integrals. This is an integration method that reverses the chain rule for derivatives.

Examples include (a) int x(1+x^2)^3 dx, (b) int x^6 cos(2x^7) dx, (c) int sin(x)cos(x) dx, and (d) int x(1+x)^2 dx. In problem (c), we recall an occasional problem with integrals, and, in problem (d), we show an instance where re-substitution is required.

Tagged under: Mathematics,calculus,antiderivative,integration,substitution,indefinite,integral,chain,rule

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