What is the integral of 2sqrt(y) ?

The integral of 2sqrt(y) is 4/3 y^{3/2}+C

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integral of 2sqrt(y)

\int 2 y d y

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

Solution steps

\int 2 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 d y

Apply the Power Rule

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

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

Simplify

2 \cdot \frac{2}{3} y^{\frac{3}{2}} : \frac{4}{3} y^{\frac{3}{2}}

= \frac{4}{3} y^{\frac{3}{2}}

Add a constant to the solution

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

\int x sin^{2} (7 x) d x

f (x) = \frac{2}{x}, (3, \frac{2}{3})

f (x) = \frac{x + 6}{x - 4}

1 + x

y = (4 x - 1)^{2}