$$\int_{-\infty}^{\infty}\left(\sin ^{2} x+2 \tan x\right) \delta^{\prime}(x)$$
$1.$ Is this integral missing a $dx$ at the end?
$2.$ Assuming that it is then performing integration by parts leaves me with $$
\left.\left[(\sin ^{2}(x)+2 \tan (x)\right) \delta(x)\right]_{-\infty}^{\infty}-\int_{-\infty}^{\infty} 2[\cos (x)\sin(x)+\sec^2(x)] \delta(x) d x
$$
But how does one evaluate the left hand side?
Best Answer
* Here I mean either "$f$ is compactly supported smooth and $d$ is a distribution" or "$f$ is Schwarz class and $d$ is a tempered distribution".