let $\displaystyle

f(x) = \left[ {\int\limits_0^x {e^{ - t^2 } dt} } \right]^2 \,\,\,\,\,\,g(x) = \left[ {\int\limits_0^1 {e^{ - x^2 (1 + t^2 )} } \cdot \frac{1}{{(1 + t^2 )}}} \right]^2

$

show that $\displaystyle

f'(x) + g'(x) = 0

$

and show that $\displaystyle

f(x) + g(x) = \frac{\pi }{4}

$

finally prove that $\displaystyle

\int\limits_0^\infty {e^{ - t^2 } dt} = \frac{{\sqrt \pi }}{2}

$

i cant seem able to show that f'(x)+g'(x)=0, i think its beacause i cant derivate g(x). Help plz