19.
\(\int\dfrac{2e^x}{e^x+3}dx=2\int\dfrac{d\left(e^x+3\right)}{e^x+3}dx=2ln\left|e^x+3\right|+C\)
\(\Rightarrow T=3-2+2019=2020\)
20.
\(\int xdx+\int x\sqrt{x^2+1}dx=\dfrac{1}{2}x^2+\dfrac{1}{2}\int\sqrt{x^2+1}.d\left(x^2+1\right)\)
\(=\dfrac{x^2}{2}+\dfrac{1}{3}\sqrt{\left(x^2+1\right)^3}+C\)
\(\Rightarrow a+b+c=2+1+3\)
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