What is the integral of 2ysqrt(y) ?

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

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integral of 2ysqrt(y)

\int 2 y y d y

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

Solution steps

\int 2 y y d y

Take the constant out:

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

= 2 \cdot \int y y d y

Simplify

y y : y^{\frac{3}{2}}

= 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

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