Let f(x)=∫ (d x)/(x^(2/3)+2 x^(1/2)) be such that f(0)=-26+24 log_e (2). If f(1)= a + b log_e (3), where a, b ∈ Z, then a + b is equal to:

Let $\displaystyle f(x)=\int \frac{\mathrm{d} x}{x^{\left(\frac{2}{3}\right)}+2 x^{\left(\frac{1}{2}\right)}}$ be such that $\displaystyle f(0)=-26+24 \log _{\mathrm{e}}(2)$. If $\displaystyle f(1)=\mathrm{a}+\mathrm{b} \log _{\mathrm{e}}(3)$, where $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{Z}$, then $\displaystyle \mathrm{a}+\mathrm{b}$ is equal to: