Definite integral/sqrt(x) - 1 over sqrt(x) +1 over (2x+3)-e^(-x)/1 to 4/Exercise

Compute the definite integral of the function

$f\colon \mathbb {R} _{+}\longrightarrow \mathbb {R} ,x\longmapsto f(x)={\sqrt {x}}-{\frac {1}{\sqrt {x}}}+{\frac {1}{2x+3}}-e^{-x},$

on ${}[1,4]$.

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