5.5 The Substitution Rule/61

$\int _{0}^{13}{\frac {dx}{\sqrt[{3}]{(1+2x)^{2}}}}$ = $\int _{0}^{13}{\frac {1}{2^{3}{\sqrt {t^{2}}}}}dt$ = ${\frac {1}{2}}\int _{0}^{13}{\frac {1}{\sqrt[{3}]{t^{2}}}}dt$ = ${\frac {1}{2}}\int _{0}^{13}{\frac {1}{t^{\frac {2}{3}}}}dt$ = ${\frac {1}{2}}3{\sqrt[{3}]{t}}$ = ${\frac {1}{2}}3{\sqrt[{3}]{1+2x}}$ = ${\frac {3}{2}}{\sqrt[{3}]{1+2x}}$ = ${\frac {3}{2}}{\sqrt[{3}]{1+2x}}{\bigg |}_{0}^{13}$ = ${\frac {3}{2}}{\sqrt[{3}]{1+2x*13}}-{\frac {3}{2}}{\sqrt[{3}]{1+2*0}}$ = Failed to parse (syntax error): {\displaystyle \3}