Let \(F(x)\) be the antiderivative of \(\dfrac{(\ln x)^3}{x} \). If \(F(1)=0\), then \(F(5)=\)

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We can simply evaluate the definite integral in our calculator.

$$ F(5) = F(1) + \int \limits_1^5 \frac{(\ln x)^3}{x} $$ $$ F(5) \approx 0 + 1.677 $$ $$ = \boxed{1.677} $$

\(u\)-substitution can be used to find the equation for \(F(x)\). Solving for \(F(5)\) will still require a calculator.