[Solved] Same size for equation over multiple lines with norm

Annie Asks: Same size for equation over multiple lines with norm
I want to have an equation written over multiple lines but without the sizes varying too much. An example would be

Code:
begin{align*}
||f||&=||(tmapstoint_0^t g(s)ds)||+||A||\
     &leq a+b
end{align*}

The problem then is:
-The norm signs are too small. This can be changed by using left, right and middle but then the left hand side is of a different size
-Or integral sign is very small if I use textstyle to compress it’s size

A solution which could look nice would be something like

Code:
begin{align*}
||f||&=left|middle|middle(tmapstotextstyle{int_0^t} g(s)dsmiddle)middle|middle|+middle|middle|A|right|\
     &leq a+b
end{align*}

However it still looks strange as the left hand side is still small and I don’t know how this could be changed. Are there any recommendations how to write such equations aesthetically?

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