Substitution 1. If the integrand contains ''a''² − ''x''², let
: $x\; =\; a\; \backslash sin(\backslash theta)$
and use the identity
: $1-\backslash sin^2(\backslash theta)\; =\; \backslash cos^2(\backslash theta).$

Substitution 2. If the integrand contains ''a''² + ''x''², let
: $x\; =\; a\; \backslash tan(\backslash theta)$
and use the identity
:$1+\backslash tan^2(\backslash theta)\; =\; \backslash sec^2(\backslash theta).$

Substitution 3. If the integrand contains ''x''² − ''a''², let
:$x\; =\; a\; \backslash sec(\backslash theta)$
and use the identity
:$\backslash sec^2(\backslash theta)-1\; =\; \backslash tan^2(\backslash theta).$