The Second Fundamental Theorem of Calculus Question 4

For $x\gt 0$, $\dfrac{d}{dx}\left(\int\limits_0^{3x}\ln(t^3+1) dt\right) =$

$\ln(x^3+1) $

$\ln(27x^3+1) $

$3\ln(x^3+1) $

$3\ln(27x^3+1) $

Approach

$$ \frac{d}{dx}\left(\int\limits_0^{3x}\ln(t^3+1) dt\right) $$ $$ = \ln((3x)^3+1) \cdot \frac{d}{dx}(3x) $$ $$ = \boxed{3\ln(27x^3+1)} $$