Question

d/dx 0∫x √1+a^3 da i need help badly

Answer 1

Looks like the derivative of an integral,

$\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\sqrt{1+a^3}\,\mathrm da$

Recall the fundamental theorem of calculus:

$\displaystyle\frac{\mathrm d}{\mathrm dx}\int_c^{f(x)}g(u)\,\mathrm du=g(f(x))f'(x)$

where $c$ is some constant.

Directly applying the theorem here gives the derivative,

$\boxed{\sqrt{1+x^3}}$