What is the integral of sqrt(8y) ?

The integral of sqrt(8y) is (4sqrt(2))/3 y^{3/2}+C

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integral of sqrt(8y)

\int 8 y d y

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

Solution steps

\int 8 y d y

Simplify

8 y : 22 y

= \int 22 y d y

Take the constant out:

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

= 22 \cdot \int y d y

Apply the Power Rule

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

= 22 \frac{2}{3} y^{\frac{3}{2}}

Simplify

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

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

Add a constant to the solution

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

m = 2 \sum \infty \frac{5}{6 ^{m}}

y^{^{'}} = 8 x^{6} y - y, y (1) = - 4

\frac{3 x}{x}

\int \frac{3}{( z ^{2} + 4 ) ( z + 1 ) ^{2}} d z

\int cos (x) sin (2 x) d x

What is the integral of sqrt(8y) ?
The integral of sqrt(8y) is (4sqrt(2))/3 y^{3/2}+C