This will sound a little odd, for we nromally say around here that we want to remove distortions in the tax system. One obvious such distortion being that capital gains and income are taxed at different rates, leading to everyone who can manage it shifting income over into capital gains. However, we don't want to rush off and try to equalise those rates. The reason being the following :
What we mean by "integrated" here is the combination of the corporation tax and the capital gains tax. A share goes up in value as the company makes more profits. But it's post tax profits that do this, not pre tax. So the higher the corporation tax the less the share price will rise: thus the lower the capital gain that the shareholder will receive.
We should thus look at the interplay of both taxes on the amount that the shareholder receives for putting their money at risk. Which is exactly what this "integrated" rate is. And that's with CGT at the current rate of 28%, not the income tax rate of 45% (the tippy top rate that is). So, if we moved CGT up to the marginal income tax rate then capital gains would be more heavily taxed than income because of that bite already taken by corporation tax. And that's absolutely not what we want to happen at all: for we know that capital taxation has higher deadweight costs than income tax anyway.
There is one way to do it though. If we abolish corporation tax altogether and simply tax dividends and capital gains as the income they are then we will indeed have equal rates for all types of income. Plus, what joys, all the spivs trying to dodge taxes through manipulation of the corporate tax system go out of business. And tens of thousands of our most highly paid lawyers and accountants have to do something productive with their lives.
What's not to like? Abolish corporation tax and then tax all income as income?