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

The integral of y^2(y+2/3) is 1/9 y^3(3y+2)-(y^4)/(12)+C

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integral of y^2(y+2/3)

\int y^{2} (y + \frac{2}{3}) d y

\frac{1}{9} y^{3} (3 y + 2) - \frac{y ^{4}}{12} + C

Solution steps

\int y^{2} (y + \frac{2}{3}) d y

Apply Integration By Parts

: \frac{1}{9} y^{3} (3 y + 2) - \int \frac{y ^{3}}{3} d y

= \frac{1}{9} y^{3} (3 y + 2) - \int \frac{y ^{3}}{3} d y

\int \frac{y ^{3}}{3} d y = \frac{y ^{4}}{12}

= \frac{1}{9} y^{3} (3 y + 2) - \frac{y ^{4}}{12}

Add a constant to the solution

= \frac{1}{9} y^{3} (3 y + 2) - \frac{y ^{4}}{12} + C

f (x) = - 4 cos (2 x)

\int - \frac{1}{e ^{x}} d x

x \to - 2 lim (1 - x^{2})

\int \frac{x + 2}{x ^{2} + 16} d x

\frac{d}{d x} (\frac{1}{x ^{25}})

What is the integral of y^2(y+2/3) ?
The integral of y^2(y+2/3) is 1/9 y^3(3y+2)-(y^4)/(12)+C