<s>[INST] can't figure out what I been doing wrong on simple integration question $$\int_0^1 \sqrt{(\sqrt{5})^2+(2t)^2}\;dt$$
Based on the formula 
$\int \sqrt{a^2+x^2}\;dx=\frac{1}{2}[x\sqrt{a^2+x^2}+a^2\log(x+\sqrt{a^2+x^2})]$
I just plug in above input into the formula above
However I can only find $3+\frac{5}{2}\log(5)$
but answers that I get from Mathematica is $\frac{3}{2}+\frac{5}{8}\log(5)$
i been trying to figuring out what I been doing wrong for days but I still can't find out what I been doing wrong.
Appreciate if someone can show what I'm been doing wrong
 [/INST] we have
\begin{align*}
  \int_0^1 \sqrt{5 + (2t)^2}\, dt &= \frac 12 \int_0^2 \sqrt{5 + x^2}\, dx\\
        &= \frac 14\left[x\sqrt{5 + x^2} + 5\log\bigl(x + \sqrt{5 + x^2}\bigr)\right]_0^2\\
        &= \frac 14\left(6 + 5\log 5 - 0 - 5 \log \sqrt 5\right)\\
        &= \frac 32 + \frac 58 \, \log 5.
\end{align*}
I don't know what you did wrong ;-), because I don't know what you did at all,
</s>