5.3 The Fundamental Theorem of Calculus/53

$g(x)=\int _{2x}^{3x}{\frac {u^{2}-1}{u^{2}+1}}du$

${\frac {d}{dx}}g(x)={\frac {d}{dx}}\left[\int _{2x}^{3x}{\frac {u^{2}-1}{u^{2}+1}}du\right]=(3*{\frac {3x^{2}-1}{3x^{2}+1}})-(2*{\frac {2x^{2}-1}{2x^{2}+1}})$

$=(3*{\frac {9x^{2}-1}{9x^{2}+1}})-(2*{\frac {4x^{2}-1}{4x^{2}+1}})$=

$=({\frac {3(9x^{2}-1)}{9x^{2}+1}})-({\frac {2(4x^{2}-1)}{4x^{2}+1}})$