Question

d/dx ∫_1^2x▒〖〖tg〗^3 tdt〗

Answer 1

Sea 
               $\displaystyle F(x)=\int _{1}^{x}\tan ^3 t \;dt$

entonces

               $\displaystyle \int _{1}^{2x}\tan ^3 t \;dt=F(2x)\\ \\ \\ \dfrac{d}{dx}\int _{1}^{2x}\tan ^3 t \;dt=2F'(2x)\\ \\ \\ \boxed{\dfrac{d}{dx}\int _{1}^{2x}\tan ^3 t \;dt=2\tan^32t}$