Exercise
$\int_{0.46}^{0.57}\left(\sqrt{1+x^3}\right)dx$
Step-by-step Solution
1
The integral $\int\sqrt{1+x^3}dx$ is non-elementary
$\left[\frac{2}{5\sqrt{x^3+1}}\left(x^4+\sqrt[6]{-1}\cdot 3^{\frac{3}{4}}\sqrt{\sqrt[6]{-1}\left(x+1\right)}\sqrt{x^2-x+1}F\left(\arcsin\left(\frac{\sqrt{- -1^{\frac{5}{6}}\left(x+1\right)}}{\sqrt[4]{3}}\right)\Big\vert \sqrt[3]{-1}\right)+x\right)\right]_{0.46}^{0.57}$
Final answer to the exercise
$\left[\frac{2}{5\sqrt{x^3+1}}\left(x^4+\sqrt[6]{-1}\cdot 3^{\frac{3}{4}}\sqrt{\sqrt[6]{-1}\left(x+1\right)}\sqrt{x^2-x+1}F\left(\arcsin\left(\frac{\sqrt{- -1^{\frac{5}{6}}\left(x+1\right)}}{\sqrt[4]{3}}\right)\Big\vert \sqrt[3]{-1}\right)+x\right)\right]_{0.46}^{0.57}$