What is the integral of 2y^{3/2} ?

The integral of 2y^{3/2} is 4/5 y^{5/2}+C

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integral of 2y^{3/2}

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: \frac{2}{5} y^{\frac{5}{2}}

= 2 \cdot \frac{2}{5} y^{\frac{5}{2}}

Simplify

2 \cdot \frac{2}{5} y^{\frac{5}{2}} : \frac{4}{5} y^{\frac{5}{2}}

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

Add a constant to the solution

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

\int tan (8 x + 1) d x

\int \frac{3 arctan ( x )}{x ^{2}} d x

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

\frac{d y}{d x} + a y - b = 0

f (x) = 5 x^{2} - 4 x - 2, at x = 1