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I am suppose to determine if the following rule is a distribution $$\langle u,\phi \rangle = \int_0^1 \frac{u(x)}{x} \, dx$$ and then also $$\langle u,\phi \rangle = \int_{-\infty}^\infty \phi + 1 \, dx.$$ The notation is throwing me off. At first I thought I had to show ## \langle Au + Bu,\phi \rangle = A\langle u,\phi \rangle + B\langle u,\phi \rangle ## but then the next question did not depend on ##u##, so I'm a little confused. Can someone clarify the notation please?