For the case that a function has multiple roots, (fleft(x_{i} ight)=0, i=1,2, ldots), it can be shown

For the case that a function has multiple roots, \(f\left(x_{i}\right)=0, i=1,2, \ldots\), it can be shown that

\[\delta(f(x))=\sum_{i=1}^{n} \frac{\delta\left(x-x_{i}\right)}{\left|f^{\prime}\left(x_{i}\right)\right|}\]

Use this result to evaluate \(\int_{-\infty}^{\infty} \delta\left(x^{2}-5 x-6\right)\left(3 x^{2}-7 x+2\right) d x\).