Ejercicio
$\int_1^{2x}\left(\sqrt{1+t^3}\right)dt$
Solución explicada paso por paso
1
La integral $\int\sqrt{1+t^3}dt$ es no elemental
$\left[\frac{2}{5\sqrt{t^3+1}}\left(t^4+\sqrt[6]{-1}\sqrt[4]{\left(3\right)^{3}}\sqrt{\sqrt[6]{-1}\left(t+1\right)}\sqrt{t^2-t+1}F\left(\arcsin\left(\frac{\sqrt{-\sqrt[6]{\left(-1\right)^{5}}\left(t+1\right)}}{\sqrt[4]{3}}\right)\Big\vert \sqrt[3]{-1}\right)+t\right)\right]_{1}^{2x}$
Respuesta final al problema
$\left[\frac{2}{5\sqrt{t^3+1}}\left(t^4+\sqrt[6]{-1}\sqrt[4]{\left(3\right)^{3}}\sqrt{\sqrt[6]{-1}\left(t+1\right)}\sqrt{t^2-t+1}F\left(\arcsin\left(\frac{\sqrt{-\sqrt[6]{\left(-1\right)^{5}}\left(t+1\right)}}{\sqrt[4]{3}}\right)\Big\vert \sqrt[3]{-1}\right)+t\right)\right]_{1}^{2x}$