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

The integral of y^2(y^2-3) is (y^5)/5-y^3+C

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integral of y^2(y^2-3)

\int y^{2} (y^{2} - 3) d y

\frac{y ^{5}}{5} - y^{3} + C

Solution steps

\int y^{2} (y^{2} - 3) d y

Expand

y^{2} (y^{2} - 3) : y^{4} - 3 y^{2}

= \int y^{4} - 3 y^{2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y^{4} d y - \int 3 y^{2} d y

\int y^{4} d y = \frac{y ^{5}}{5}

\int 3 y^{2} d y = y^{3}

= \frac{y ^{5}}{5} - y^{3}

Add a constant to the solution

= \frac{y ^{5}}{5} - y^{3} + C

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What is the integral of y^2(y^2-3) ?
The integral of y^2(y^2-3) is (y^5)/5-y^3+C