Integral of \( \displaystyle 3 x^{2} - 4 x + 1 \)

Problem 4.195 · medium

1. \[ \int \left(3 x^{2} - 4 x + 1\right)\, dx \]
   integralStart with the integral of the polynomial.✓ Proved
2. \[ = \int 1\, dx - \int 4 x\, dx + \int 3 x^{2}\, dx \]
   linearitySplit the integral into three separate terms.✓ Proved
3. \[ = \int 1\, dx - 4 \int x\, dx + 3 \int x^{2}\, dx \]
   linearityPull out the constant coefficients.✓ Proved
4. \[ = x^{3} - 2 x^{2} + x \]
   antiderivative simplifyApply the power rule to each term. Simplify the coefficients.✓ Proved