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I = integral (6x2 - 4x) dx

July 16, 2026Mathematics

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Answer

\mathbf{2x^3 - 2x^2 + C}

Step-by-step solution

3 steps

Separate the integral into individual terms.
$I = \int (6x^2 - 4x) \,dx = \int 6x^2 \,dx - \int 4x \,dx$
Apply the power rule for integration, $\int x^n \,dx = \frac{x^{n+1}}{n+1} + C$ , to each term.
$I = 6 \cdot \frac{x^{2+1}}{2+1} - 4 \cdot \frac{x^{1+1}}{1+1} + C$ $I = 6 \cdot \frac{x^3}{3} - 4 \cdot \frac{x^2}{2} + C$
Simplify the expression.
$I = 2x^3 - 2x^2 + C$
The final answer is $\mathbf{2x^3 - 2x^2 + C}$ .

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