What is the integral of (x^3-27)x^2 ?

The integral of (x^3-27)x^2 is 1/3 x^3(x^3-27)-(x^6)/6+C

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integral of (x^3-27)x^2

\int (x^{3} - 27) x^{2} d x

\frac{1}{3} x^{3} (x^{3} - 27) - \frac{x ^{6}}{6} + C

Solution steps

\int (x^{3} - 27) x^{2} d x

Apply Integration By Parts

: \frac{1}{3} x^{3} (x^{3} - 27) - \int x^{5} d x

= \frac{1}{3} x^{3} (x^{3} - 27) - \int x^{5} d x

\int x^{5} d x = \frac{x ^{6}}{6}

= \frac{1}{3} x^{3} (x^{3} - 27) - \frac{x ^{6}}{6}

Add a constant to the solution

= \frac{1}{3} x^{3} (x^{3} - 27) - \frac{x ^{6}}{6} + C

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What is the integral of (x^3-27)x^2 ?
The integral of (x^3-27)x^2 is 1/3 x^3(x^3-27)-(x^6)/6+C