What is the integral of x^2(6-x^3) ?

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

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integral of x^2(6-x^3)

\int x^{2} (6 - x^{3}) d x

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

Solution steps

\int x^{2} (6 - x^{3}) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} (6 - x^{3}) - \int - x^{5} d x

= \frac{1}{3} x^{3} (6 - x^{3}) - \int - x^{5} d x

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (cos^{2} (2 x + 1))

\int \frac{3}{5} d x

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 2 yz)

\frac{d}{d x} (d y (d, x))

\frac{7}{x}, 4

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