Substitution with a given u

Problem 4.317 · hard

1. \[ \frac{d}{d x} \ln{\left(x \right)} = \frac{1}{x} \]
   So du = dx/x.✓ Proved
2. In terms of u the integral becomes ∫ 3*u**4 du.
   Reviewed
3. \[ \frac{d}{d u} \frac{3 u^{5}}{5} = 3 u^{4} \]
   An antiderivative in u is 3*u**5/5; differentiating confirms it.✓ Proved
4. \[ \frac{3 \ln{\left(x \right)}^{5}}{5} \]
   Replace u by log(x).✓ Proved
5. \[ \frac{d}{d x} \frac{3 \ln{\left(x \right)}^{5}}{5} = \frac{3 \ln{\left(x \right)}^{4}}{x} \]
   Differentiating the answer returns the integrand.✓ Proved