Integral of \( \displaystyle - 12 x + 3 \left(3 x + 1\right)^{2} - 3 \)

Problem 4.361 · medium

1. \[ \int \left(- 12 x + 3 \left(3 x + 1\right)^{2} - 3\right)\, dx \]
   simplifyStart with the integral of the given expression.✓ Proved
2. \[ = \int \left(27 x^{2} + 6 x\right)\, dx \]
   algebra algebra simplifyExpand the squared binomial. Distribute the 3 into the parentheses. Combine like terms.✓ Proved
3. \[ = \int 6 x\, dx + \int 27 x^{2}\, dx \]
   linearitySplit the integral into two parts.✓ Proved
4. \[ = 9 x^{3} + 3 x^{2} \]
   antiderivativeIntegrate each term using the power rule.✓ Proved