What is the integral of 9x^3y+3y^2 ?

The integral of 9x^3y+3y^2 is 3y^2x+(9yx^4)/4+C

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integral of 9x^3y+3y^2

\int 9 x^{3} y + 3 y^{2} d x

3 y^{2} x + \frac{9 y x ^{4}}{4} + C

Solution steps

\int 9 x^{3} y + 3 y^{2} d x

Apply the Sum Rule:

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

= \int 3 y^{2} d x + \int 9 y x^{3} d x

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

\int 9 y x^{3} d x = \frac{9 y x ^{4}}{4}

= 3 y^{2} x + \frac{9 y x ^{4}}{4}

Add a constant to the solution

= 3 y^{2} x + \frac{9 y x ^{4}}{4} + C

x \to 0 - lim (4 (\frac{1}{x} - csc (x)))

\frac{d}{d x} ((\frac{1}{3}) (x^{2} + 2)^{\frac{3}{2}})

\frac{\partial}{\partial x} (2 y - x^{2} e^{- y})

t^{3} e^{b \cdot t}

\frac{\partial}{\partial x} (ln (x + y^{4}))

What is the integral of 9x^3y+3y^2 ?
The integral of 9x^3y+3y^2 is 3y^2x+(9yx^4)/4+C