Integral of \( \displaystyle - 8 x + 3 \left(2 x - 1\right)^{2} + 5 \)

Problem 4.193 · medium

1. \[ \int \left(- 8 x + 3 \left(2 x - 1\right)^{2} + 5\right)\, dx \]
   integralStart with the integral of the given expression.✓ Proved
2. \[ = \int \left(12 x^{2} - 20 x + 8\right)\, dx \]
   algebra algebra simplifyExpand the squared binomial. Distribute the 3 into the parentheses. Combine like terms.✓ Proved
3. \[ = \int 8\, dx - \int 20 x\, dx + \int 12 x^{2}\, dx \]
   linearitySplit the integral into three parts.✓ Proved
4. \[ = 4 x^{3} - 10 x^{2} + 8 x \]
   antiderivativeIntegrate each term using the power rule.✓ Proved