Question

D/dx 0∫x √1+a^3 da i need help badly

Answer 1

Looks like the derivative of an integral,

`\displaystyle(\mathrm d)/(\mathrm dx)\int_0^x√(1+a^3)\,\mathrm da`

Recall the fundamental theorem of calculus:

`\displaystyle(\mathrm d)/(\mathrm dx)\int_c^(f(x))g(u)\,\mathrm du=g(f(x))f'(x)`

where
`c` is some constant.

Directly applying the theorem here gives the derivative,

`\boxed{√(1+x^3)}`