What is the integral of (y^4+2y^2)/(sqrt(y)) ?

The integral of (y^4+2y^2)/(sqrt(y)) is 2/9 y^{9/2}+4/5 y^{5/2}+C

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integral of (y^4+2y^2)/(sqrt(y))

\int \frac{y ^{4} + 2 y ^{2}}{y} d y

\frac{2}{9} y^{\frac{9}{2}} + \frac{4}{5} y^{\frac{5}{2}} + C

Solution steps

\int \frac{y ^{4} + 2 y ^{2}}{y} d y

Expand

\frac{y ^{4} + 2 y ^{2}}{y} : \frac{y ^{4}}{y} + \frac{2 y ^{2}}{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 \frac{y ^{4}}{y} d y + \int \frac{2 y ^{2}}{y} d y

\int \frac{y ^{4}}{y} d y = \frac{2}{9} y^{\frac{9}{2}}

\int \frac{2 y ^{2}}{y} d y = \frac{4}{5} y^{\frac{5}{2}}

= \frac{2}{9} y^{\frac{9}{2}} + \frac{4}{5} y^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{9} y^{\frac{9}{2}} + \frac{4}{5} y^{\frac{5}{2}} + C

f (x) = arccsc (3 x)

\frac{\partial}{\partial x} (sin (4 x^{3} y - 5 x y^{4}))

x \to 4 lim (7^{x} + 12 x)

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

y = 6^{x}

What is the integral of (y^4+2y^2)/(sqrt(y)) ?
The integral of (y^4+2y^2)/(sqrt(y)) is 2/9 y^{9/2}+4/5 y^{5/2}+C