$\int x^{2}(2 x-2) d x=\frac{x^{4}}{2}-\frac{2 x^{3}}{3}+C$ .

Name: $\int x^{2}(2 x-2) d x=\frac{x^{4}}{2}-\frac{2 x^{3}}{3}+C$ .
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Question

Quizplus · Accepted Answer

Expanding the integrand gives $\int (2x^3 - 2x^2) dx = \frac{2x^4}{4} - \frac{2x^3}{3} + C = \frac{x^4}{2} - \frac{2x^3}{3} + C$, which matches the given expression.

∫x2(2x−2)dx=x42−2x33+C\int x^{2}(2 x-2) d x=\frac{x^{4}}{2}-\frac{2 x^{3}}{3}+C∫x2(2x−2)dx=2x4​−32x3​+C

$\int x^{2}(2 x-2) d x=\frac{x^{4}}{2}-\frac{2 x^{3}}{3}+C$